Use the guidelines to sketch the curve  y = 2 x2  / ( x 2  -1 )

Q: Find the points on the curve y = x4- 6x2 + 4 where the tangent line is horizontal.

A: y=x4-6x2+4 Differentiating with respect to x, we get dydx=4x3-62x+0=4x3-12x Now the tangent line is…

Q: Find an equation of the line tangent to the graph of y = exat x = 0.

A:

Q: Use the guidelines of this section to sketch the curve.   y = 2√ x    -x

A: We will make a table for the function  x 0 1 4 9 y 0 1 0 -3

Q: Determine the equation of the tangent line to the curve y = (2x2 - 3x)3 at x = 2.

A: To find the equation of the tangent line

Q: Write the equation of the tangent line to the curve y = x3 + 3x - 8 at (2, 6).

A: To find the equation of the tangent line to the curve y=x3+3x-8 at (2,6). Solution: We know, The…

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have horizontal tangent line.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find the equation of the tangent line to the curve y=5x³-1 at x= -1.

A:

Q: the guidelines of this section to sketch the curve: y = x+ – 8x

A:

Q: Find the equation of the tangent line to the curve at the given point. y = 9x - 8Vx, (1, 1) %3D

A:

Q: Write the equation of the tangent line to the graph of y = x2 at the point where x = 2.5.

A: To find the tangent line to a function at a given point first find the first derivative of the…

Q: Suppose a curve is defined by the equati on y2 = x*(2- x). What is the equation of the line tangent…

A: Given curve

Q: Find an eqaution of the tangent line to the curve at the given point. y = 4x - 3x2, (2,-4)

A: The given function is y=4x-3x2 and the point is 2,-4

Q: Find an equation of the tangent line to the curve y 9tanx at the point %3D

A:

Q: Describe the tangent line at an arbitrary point on the graph of y = 2x + 8

A: we have to describe the tangent line at an arbitrary point on the graph of y=2x+8

Q: Write the equation of the tangent line to the curve (a lemniscate) 2(x2 + y²)“ = 25(x² – y²) at the…

A:

Q: at what point is the tangent line y3=2x2 perpendicular to the line x-y-1=0? P=(?,?)

A:

Q: Write the equation of the tangent line to the curve = 2 at the point (1,1). .3

A:

Q: Find an equation of the tangent line to the curve at the given point. y = 2x3 – x2 + 4, (2,16) y =

A:

Q: Use the guidelines of this section to sketch the curve   y =2 sqrt x - x

A: Given              y=2x-x

Q: Find an equation of the tangent to the curve f(x) = /x+ 7 that has slope %3D 4

A:

Q: Find the equation of the tangent line to the curve y=(x-2) (x+1)? at point (3, 16).

A:

Q: The tangent line to the curve y = x3 - 6x2 - 34x - 9 has slope 2 at two points on the curve. Find…

A: Given,  The tangent line to the curve y=x3-6x2-34x-9 has Slope=2 at two points on the curve.…

Q: Find an equation of the tangent line to the curve y=8ln((x^3)-26) at the point (3,0).

A: To determine equation of tangent line at given point.

Q: Find the equation of the tangent line to the curve y = 3x2 – x at the point (1,2). y =

A:

Q: Use the guidelines of this section to sketch the curve. х — 6 y = x2

A:

Q: Find the point f(x)= x3 - 3x2 + x + 4 where the tangent line has slope 10

A:

Q: 6. What is the slope of the tangent line to the inflection point of the curve y = x3 – 4x2 - 3x – 6?

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find an equation of the tangent line to the curve y = 2x ^ 2 + 1 that is parallel to the line 8x -…

A: Given: the curve y=2x2+1 and the line is parallel to 8x-y+3=0 The equation of line tangent to the…

Q: Determine the values of x where a curve y=x³-3x²-9x+12 has horizontal tangent lines

A: Given,y=x3-3x2-9x+12differentiating both the sides w.r.t. xdydx=ddxx3-3x2-9x+12dydx=3x2-6x-9

Q: Find the points on the graph of y = ex where the tangent line has slope 4.

A:

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have vertical tangent line.

A: This question is taken from the tangent and line in which we have to all points on the graph that…

Q: Write an equation of the tangent line to the curve x2+y2-25=0 at the point (3,4).

A:

Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: Find an equation of the tangent line to the curve x^(2/3)+y^(2/3)=13 at the point (−27,−8).

A: Given:

Q: Find an equation of the tangent line to the curve at the given point. y = 2x2 - 6x + 1, (4, 9) y =

A: First find slope at given value then equation of tangent line

Q: Find the tangent and normal line to the curve at the specified condition.  3x3 - x2 - 12x + 6 at…

A: Suppose we wish to find the equation of the tangent tof(x) = 3x3 − x2 - 12x +6 the points where the…

Q: Find the equation of the tangent line to the curve y = In(x³ – 63) at the point (4, 0). Tangent Line…

A:

Q: Write the equation of the tangent line to the curve y = x + 6x - 3 at (1,4).

A: Given,           The curve is y=x2+6x-3 and the point is 1,4.To find: The equation of the tangent…

Q: Use the guidelines of this section to sketch the curve   y = x e -x

A: Consider the given function as y=xe-x

Q: Write the equation of the tangent line to the graph of y = x at the point x = - 0.7.

A:

Q: Show that the curve y =6x3 +5x -3 has no tangentline with slope 4.

A: Consider the following equation of curve: y=6x3+5x-3 Differentiate y with respect to x:…

Q: Find an equation of the tangent line to the curve at the given point. y = 2x2 - 8x + 1, (5, 11) y =…

A: To find: The equation of tangent to the curve y=2x2-8x+1 at 5,11. Given: The equation of curve is…

Q: Show that the curve y = 6 x 3 + 5x -3            has no tangent line with slope 4.

A: y=6x3+5x-3 has no tangent line with slope 4

Q: Find the equation of the tangent line to the curve y = x³ – 4x + 3 at the point (3, 18). Tangent…

A: Answer and explanation is given below...

Q: Find the equations of the tangent lines of the curve y = that have slope 1+ 2r

A: Given data:   The expression for the curev is: y=2x1+2x. The given slope of the curve is: m=2/9.…

Q: Find the equation of the tangent line to the curve y = In(x³ – 26) at the point (3, 0). Tangent Line…

A: The solution is as follows:

Q: Determine the slope of the tangent line to the curve (x² + y² – 2x)² = 2(x² + y²) at (2, 2).

A:

Q: Find an equation of the tangent line to the curve at the given point. y = 2x³x² + 2, (1, 3) y = 6x²…

A:

Q: Determine the slope of the tangent line to the curve y=2 – x2 at the point (3,-7)

A: slope of tangent = slope of given curve  step 1  we have to find slope of curve  slope = dy/dx  so…

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: