Suppose that  ff"' is continuous and f'(c)  =f"(c) =0 , but f"'(c) >0. Does f have a local maximum or minimum at c? Does f have a point of inflection at  c?

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

A:

Q: Find a first degree approximation of f (x) = In x centered at x = 1.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use the given derivative to find all critical points off, and at each critical point determine…

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Q: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

Q: b) Suppose that f(x) 1 if x is negative. Can ƒ be continuous at x = 0?

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Q: Determine whether the following statement is true or false, and explain why. The absolute maximum of…

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Q: Show that the function f(x, y) x4 + y? has no limit as (x, y) approaches (0,0).

A: Note: Since we can solve at most one problem at a time, we have solved the first one. Kindly…

Q: The function y = 1/x does not take on either a maximum or a minimum on the interval 0 < x < 1…

A: Extreme Value Theorem:If a function f(x) is continuous on a closed interval [a,b], then f(x) has…

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: Find the equation of the tangent line of f(x) = sqrt(x+1) at x = 0 using the definition of limits.

A: To find: The equation of tangent of line. Given: The function is f(x)=x+1. Concept used: Slope…

Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

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Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, 1]?

A: follow next step

Q: Find the instananeous rate of change for f(x)= √ X at x=1 using the limit definition

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Q: What does it mean for f to be differentiable at a ?

A: we have to define that what we mean by the f is differentiable at a.

Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: Give an example of a function that is continuous on -∞ < x < o but is not differentiable at x = 3.

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Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given  f(x,y)=x2y

Q: show steps please

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Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

Q: Use the given derivative to find all critical points off, and at each critical point determine…

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Q: What is the absolute minimum value of f(x) = æ + sin a on the interval ,

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Q: H(x) = L, [At) +A-1) ]dt

A: Question derivative of function.

Q: Suppose that fx) is continuous on [0, 9] and F(x) is an anti-derivative of f. If F(0)=9 and F(9)=7,…

A: Given that:                           f(x) is continuous in [0, 9].…

Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

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Q: Prove that constant function is differentiable at ever x ER.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

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Q: The function f(x)=³ in (x) is continuous everywhere except x (х-1) at x=0 and at x=1. When…

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Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: Find the absolute extrema of the function on the closed interval. TEX y = tan 16 ), [0, 4] minimum…

A: Given that, The function is y=tanπx16 on the closed interval [0, 4]. To find absolute extrema:…

Q: Prove that if the function f : I → R has a bounded derivative on I, then f is uniformly continuous…

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Q: What is the absoluite extrema of the function h in interval [0, π]. Calculate and state the…

A: Exponential and sin, cos are always continuous

Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

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Q: The Bisection method is based on the principle that a continuous function which is positive at one…

A: Consider the provided question, We have find the value after third bisection process of the function…

Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: The given question is related with limits. Given that fx , y = 3y9x2 + 4y2 . We have to find two…

Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, ¤]?

A:

Q: Suppose f is continuous on an interval containing a critical pointc and f″(c) = 0. How do you…

A: According to the second derivative test, If c= critical value. if f''(c)&lt;0, then f(x) has local…

Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, n]?

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Q: Find the absolute maximum value on (0, oo) for f(x)37-4x--

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Show that x³, if x 0 is not continuous at x = 0. %3D

A: According to the problem, we have

Q: Is f continuous at x = 1?

A: The condition of continues function is, limx→a+fa=limx→a-fa=fa   For limit of function from the…

Q: It appears that f is not differentiable at a = 0. Moreover, the tangent line does not exist at this…

A: yes it is true.

Q: generate a continuous and differentiable function that is decreasing at -6, has a local minimum at…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: