Use the definition mtan=(f(x)-f(a))/x-a to find the slope of the line tangent to the graph of f at P. A. F(x)=x+4/x P(4,5) B. F(x)= sqrt(x-1) P(5,2)

Q: Find all points of the graph of f(x) = 3x2 + 9x whose tangent lines are parallel to the line y - 57x…

A: Solution: Two lines are parallel if they have same slope.

Q: Use the First Derivative Test to find any relative extrema of the function. (a) g(x) = 2x³ – 18x

A:

Q: Find the equation of the tangent line to the graph f(x) = 2x² + 5 at P(-1,7)

A: We will find out the required equation of tangent.

Q: b) Use the definition of the derivative to find the derivative of f(x) = 4x³ + - at a = 1. 23

A: Given: fx=4x3+1x3; x=1 We know that ddxxn=nxn-1                                          ..1

Q: Find the equation of the tangent line to the graph of f(x) = -2(3x – 1)³ at . Show work or explain…

A:

Q: What is the maximum slope of a tangent to the function f(x) -x³ + 4x - 2? ==

A:

Q: Find the derivative of the function f(x) = -8x² – 18x + 23 by definition of derivatives f(x + h) –…

A:

Q: Find the slope of the tangent line of f(x)=10x2-3 at x=-2.

A: Given f(x)=10x2-3and x=-2

Q: Find the slope m of the line tangent to the graph of the function f(x)=9-x^2 at point P(4,-7).

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Q: Find the slope-intercept equation of the tangent line to f (x) = 3x² – 4x + 5 at the point (1, 4).

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Q: find the slope of the tangent line to the graph of f at the given point f(x)=x^2-8x+2 at (2,-10)

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Q: Find all points (c, f(c)) on the graph of f(x) = x3 −3x2 where the tangent line has slope 9.

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Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 3x2 -4,…

A: The given function is fx=3x2-4 and the point is 3,23.

Q: Consider the quadratic function y=4-x². Using the limit definition, find the derivative of the…

A: To find the derivative

Q: Find the points on the graph of f (x) = x3 − 3x2 + x + 4 where the tangent line has slope 10.

A:

Q: Find the equation of the tangent line to the graph f(x)=x^4 +2x^2 -x at x=1. Write your equation in…

A: Equation of tangent line to the curve fx at point x=a is given by y-fa=f'ax-a Given curve is…

Q: Find an equation of the tangent line to the graph of f(x) = 4 - x2 at the point (-1,3).

A: Solve for the equation

Q: Find an equation of the tangent to the curve f(x) = 2x2 - 2x + 1 that has slope 2.

A:

Q: Write an equation for the tangent line to g(x) at x = 2 if g(2) = 7 and g' (2) =-3.

A: g(2)=7 and g'(2)=-3 , we have to find tangent line

Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent.

A: Given that  f(x)=(-8x)/(√(2x-1))  The function has a horizontal tangent  To find the point at which…

Q: Find the slope-intercept equation of the tangent line to the graph of f(x) = x2 at (-3, 9).

A: Consider the following function: fx=x2 Differentiate fx with respect to x: ddxfx=ddxx2f'x=2x…

Q: Use derivatives to sketch the graph of f(x) = (x² – 8x + 16)e².

A: Given

Q: Determine the point(s) at which the graph of -8x f(x) = 2х- 1 has a horizontal tangent. (х, у) %3D

A: Solution - The derivative of a function is 0 at a point where the tangent is horizontal. Let us…

Q: 4x+1 b. g(x) 9х-2

A: Given : g(x)=4x+19x-2   To Find : Derivative of g(x) using definition   NOTE:If f(x)=uv  , where u…

Q: Find the derivative of the function f(x) = 8x2 – 13x by the definition of derivatives f(x + h) –…

A: on using this formula we get = 16x-13

Q: Find the equation of the tangent line to the graph of x3 -xlny+y3=2x+5 at the point where x=2

A: x3 -xlny+y3=2x+5 To find out the equation of tangent line , we need to find out slope  Slope is the…

Q: a) Using definition, compute the derivative function of f (x) = 4x7

A: Here, we will find derivative of given function by definition of derivative,

Q: Find the equation of the tangent and normal line of the function f(x)=√2x-1 at the point (5,3)

A:

Q: 42. At what point on the graph of f(x) = -5x² + 4x – 2 is the slope of the tangent line 6?

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Q: Find the equation of the tangent line to f(x) = 4x² -5x+2 at (-1,11).

A:

Q: Find the slope of the tangent line to the graph at the given point. (x² + y²)² = 4x²y, (1, 1)

A:

Q: Find the slope of the tangent line to the graph at the given point. (x² + y²)² = 4x²y, (1,1)

A: To find slope of tangent of a curve at a given point, we need to find differential at that point

Q: Use the f'(x)=limh->0f(x+h)-f(x)/h  to find the derivative of f(x)=11x2 AT x=1

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Q: Find the equation of the tangent line to the graph of f(x) = x² – 4 at the point (3, 5). -

A: The equation of the line passing through the point (x1,y1) having slope m is given as (y-y1)…

Q: 3. Use the limit definition of the derivative to find the derivative of the function. a) f(x) = 2x²…

A: Given query is to find the derivative using definitely.

Q: Let f(x) = square root ( 4x + (3x -5)10 ).Find the equation of the tangent line to the graph of the…

A:

Q: the derivative of the function g(x) In(lx2 +21)

A: We have to find the derivative of g(x)=ln(|x2+2|)

Q: Find the point where the tangent to the graph of f(x)= -x^2-6 is parallel to the line y=4x-1

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Q: find the slope of the tangent line to the graph at the given point. (x2 + y2)2 = 4x2y,   (1,1)

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Q: Find the derivative of the function f(x) 3x2 – 12x by the definition of derivatives f(x + h) – f(x)…

A:

Q: If f(x)  = 3x2 -x3, find f'(1) and use it to find an equationof the tangent line to the curve  y=…

A: Given that, y=fx=3x2-x3      ...(1)

Q: Find the derivative of y with respect to x. y = In(x - 4) 4 -x X-4 x+4

A: The given function is  y= ln(x-4)  We have to find the derivative of y w.r.t. x

Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

A:

Q: Find the function whose tangent line has the slope 8x² + 3 for each value of x, and whose graph…

A: To find the function:

Q: Use the General Power Rule to find the derivative of the function. g(x) = V3 - 9x %3D g'(x) =

A:

Q: Find the equation of the line that is perpendicular to the tangent line to f(x) = x4+1 at x = 2 and…

A: Answer and explanation is given below

Q: Find the slope of the tangent line to the graph of the function at the given point. F(x) = 2x2 – 5,…

A:

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: