Assume that f(x) is everywhere continuous and it is given to you that f(x) + 8 lim x→2 x - 2 = -4 It follows that y = is the equation of the tangent line to y = f(x) at the point (

Q: Let f(x) tangent line to the graph of f(x) at the point (0, 0) is = 6x + 15 – 15e". Then the…

A: The given curve is: f(x)=6x+15-15ex

Q: There is no point on the graph of y = e^x at which the tangent line is parallel to 2x + y = 1. True…

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Q: If the derivative of y = f(x) at x = 2 is equal to " (0 " then y = f(x) is not continuous at r = 2.…

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Q: Let f(x) = 6x + 2 tangent line to the graph of f(x) at the point (0, – 3) is given by y = mx + b for…

A: The objective is to find the equation of the tangent line.

Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: Find all value of x=c, so that the tangent line to the graph of f(x) at (c,f(c)) will be horizontal…

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Q: Find f(x) if f(0) = 0 and the tangent line at (x, ƒ (x)) has the slope x(x² + 2}°.

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Q: Does the graph of the function y = tan x - x have any horizontal tangents in the interval 0 sx s2n?…

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Q: Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x +…

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Q: Let f(x) = V13 – x The slope of the tangent line to the graph of f(x) at the point (4, 3) is The…

A: Given ,  f(x) = √(13 - x) (A)  We have to find the slope of tangent line to the graph of f(x) at the…

Q: Does the graph of Sx²sin (1/x), x ± 0 f(x) = lo, x = 0 have a tangent line at the origin? Give…

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Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e** - 2x. f(x) = 1)et?

A: We have to find the function

Q: Find the question of the that is tangent to the curve y=-3 cos2x at x= n/6. Express with exact…

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Q: Find the equation of the tangent line to the curve f(æ)= 2x2 – x at x = 1. O T(x) =2+ 3(x – 1) O…

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Q: The tangent lines which was drawn at points A and B on the following y = f (x) function graph are…

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Q: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

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Q: The tangent line to the curve il me f(a) at 2 m 1 goes through the points y=f(x) x == and Find the…

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Q: Find the equation of the tangent line of f(x) = 8/x+3 at the point (4, 19) . Express your answer in…

A: Find the equation of the tangent line of fx=8x+3 at the pint (4,19).

Q: If f(x)=sqrt x, find the linearization L(x) at a=4. Thus the graph of L(x) would be tangent to f(x)…

A: Given information: fx=x ,  at a=4 Formula of Linearization  Lx=fa+f'ax-a

Q: ) Find the equation of the tangent line ETL for f(x) = x³ - 2x +1 at x = −1

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Q: Let f(x) = v16 – x The slope of the tangent line to the graph of f(x) at the point (7, 3) is The…

A: The slope of the tangent line to the given curve is equal to the derivative of the function at the…

Q: .The line y + 2x = 0 is tangent to y = F(x). Determine F(x) if F(x) = 4x³ + 2.

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Q: The tangent line to y = f(x) at (0, –8) passes through the point (7, 4). Compute the following. a.)…

A: Given: y = f(x) at (0,-8) Passes Point ( 7,4)

Q: Let f=sqrt(4x+3) and find the values below  1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x)/ h)…

A: Consider the given function

Q: The equation of the tangent line to f(x) = In x at x = 1 is O y = x - 1 O y = x O x = 1

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Q: 2) Find the point(s) at which the graph of f (x) = has a horizontal tangent. x2+1 %3D

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Q: The slope of the tangent line to the graph of the function y= Ttx- cotx at x=0 is O T+1 O T-1

A: Solution is given below:

Q: 4 Let f(x) = 4x + x2 given by y = mx + b for . Then the equation of the tangent line to the graph of…

A: We know that if m is slope and (x1,y1) is point on line the equation of line is given as-  (y - y1 )…

Q: Find the tangent line to f(x) = ax³ at x = -1. Assume that a is a positive constant. ***

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Q: Find a > 0 such that the tangent line to the graph of f(x) = x 2e-x at x = a passes through the…

A: fx=x2e-x Differentiating with respect to x, we get f'x=dx2dx·e-x+de-xdx·x2=2x·e-x-e-x·x2=x e-x2-x…

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: Find the equation of the tangent line to the curve y = f(x) at the given point. y = f(x) = x²-x, at…

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Q: Fin the equation of the line tangent F(x) = xcos(x) + e^x at the point (0,2)

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Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

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Q: For what vaules of x in the interval [0,2π) does the fraph of g(x)= (√3)x+2sinx+7 have a horizontal…

A: For horizontal tangent,first derivative must be zero

Q: If the tangent line to y = f(x) at (4, 2) passes through the point (0, 1), find f(4) and f'(4). f(4)…

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Q: Find an equation of the tangent line to the graph of f(x) = e×/2 In(x) at its inflection point.…

A: The point of inflection is the point where the second order derivative of the function becomes zero.…

Q: Find the slope of the tangent line to the given curve at the indicated point by using the two-step…

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Q: f(x, y) = (29 - x2 - 4y2)1/2  at  (2, 2)

A: Given that: The function f(x , y) = 29 - x2 - 4 y2   . The point (2 , 2).

Q: Find f(4) and f' (4), assuming that the tangent line to y = f(x) at a = 4 is y = -6x + 2. %3D

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Q: The tangent line to y=f(x) at (−5,−3) passes through the point (7,−3). Compute the following. a.)…

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Q: Find the equation of the tangent line to the curve of f(x) = x3 - 4x + 5 at the point (2, 5). O a. y…

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Q: Find the tangent line to y = f(x) at the point (0,–5).

A: We have to find the equation of tangent from the curve f(x) and point

Q: A curve y = f(x) defined for values of x > 0 goes through the point (1, 0) and is such that the…

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Q: Suppose the curve y=f(x) has a tangent line y=4x-5 at x=1. Consider the function g(x)=2f(x)+x+1.…

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Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: 22. If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4).…

A: #22 f(4) ? f'(4)?

Q: Find t6e eavation of tangent ine of fcx) = X+) at X=2 X-3

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Q: Find the equation of the tangent line to the curve f(x)=5-x² at x = 2. O x-4y-2=0 O 4x + y +7=0 O 4x…

A: Find the equation of the tangent line to the curve f(x) =5-x^2 at x=2.

Q: If the tangent line to the curve y = f(x) at x = c is horizontal then an extreme value of f occures…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.