GU Plot the function f(x) = x'/3. Use the zoom feature to find a 8 > 0 such that if |x – 8| < 8, then |x1/3 – 2| < 0.05.

Q: Use the first derivative to find the local max and min points.  The first derivative is  y’ = -(…

A: Solution:- It is given that  dydx=-(x2+1)(x2-1)2 for critical point  put dydx=0

Q: a(1+x²) Find the derivative 1-x

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

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Q: Dircc tion: Find the derivative of the following function: y= X1og10x %3D

A: Given function is  y = xlog10x

Q: · f(x) = In(sinh x)

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Q: Suppose f(x) = 2ax° +b°x - 4c where a, b and c are real constants. Suppose that f has a horizontal…

A: Given:- Suppose f(x) = 2ax³ + b³x-4c where a, b and e are real constants. Suppose that f has a…

Q: co find the exact values for the derivative of f at the given numbers. You

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Q: QI Find f'(x) for 1+ sec (x) S(x) 1- csc-1(x)

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Q: 9VX2 about the 7. Find the tangent line approximation for the function f (x) point x = 27. Use this…

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Q: Excrcise 1. Find the derivative y', where (3 – x) 3 Y = 1- x \ (3+ x)²

A: Given,        y=x21-x3-x3+x23

Q: f(x) = 2 arctan x + x f(x) = In(x? - 4x +5)

A: Solve the following

Q: Evaluate f sec x dx. Show your solution. Upload Choose a File

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Q: 8. Determine the intervals where the function is increasing or decreasing. Find the local maxima and…

A: First derivative test

Q: Use the second derivative to discuss concavity. The second derivative is y’’ ={2x(x2+3)}/ (x2-1)3

A: given,  y''=2xx2+3x2-13 we have to discuss the concavity using second derivative.

Q: Use the four-step process to find the slope of the tangent line to the graph of the given function…

A: In the question we have to find the slope of tangent by following the steps where the given function…

Q: A car's movement is represented by the function 2x3 + 6x2 + 2x + 3 in kilometers reco at an hourly…

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Q: 2 cosecx - cotx (a) If f(x)=: then find 1+ secx

A: According to our company policy we can answer only first question

Q: dy x? sin x dx cscy

A: Separate x and y terms ,then integrate on both sides

Q: (2xsinycosy - x+2x²evx´ )dy =(y-sin2y -4xyex)dx

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Q: Using the first and second derivatives, predict then sketch the behavior of the functions below,…

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Q: e equation implicitly defines y as a differentiable function of >

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Q: 3x2 tan x If f(x) find sec x f'(x) = Find f'(3)=

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Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

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Q: 3x2 tan x If f(x) find sec x f'(x) = %3D Find f'(3)=

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Q: 3x2 tan x If f(x) find sec x f' (x) = %3D Find f'(3)=

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Q: ip .(using implicit diflterentiation) dz For the function tan y 7a +83, find

A: To find: derivative using implicit differentiation.

Q: Given the function f(x) = 3cos(x/2), find the relative extrema on the interval (pi, 7pi) using the…

A: Given that: f(x)=3.cosx2       in (π, 7π)

Q: Find the average rate of change of the function f(x) = 1x² – 7x- 8, on the interval x E [1,5]. |…

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Q: Solve the non-linear function using NR AND Secant Method. Use 5 decimal values and stop at & S…

A: Note : As per our policy, we are allowed to answer only first part of question kindly post remaining…

Q: Find the x-coordinates of all local maxima using the second derivative test. g(x)=x 7 +3x 6 +2 If…

A: Consider the function g(x) = x7 + 3x6 + 2.Compute the first derivative of g(x) as follows.

Q: f(x)=1-x. Use the definition of the derivative to find f", f" and f""

A: Derivative by using definition

Q: 80. The function f has first derivative given by f'(x) = x* – 6x² – 8x – 3. On what intervals is the…

A: Derivative of the function f(x) is f'(x)=x4-6x2-8x-3

Q: Cosx f(x) = function is odd or even

A: A function f(x) is said to be even if f(-x)=f(x) and a function f(x) is said to be odd function if…

Q: Find the x-coordinates of all local maxima using the second derivative test. h(x) = x° – 4x + 10 If…

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Q: Use the Second Derivative Test to find all local extrema, If the test applies. Otherwise, use the…

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Q: f(x) = tanh(6x) then f'(x) =

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Q: (a) Use the Second Derivative Test to find the local extreme values of the function

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Q: Find the values of x where the tangent line is horizontal for f(x) =(x^2 + 5)^2

A: Given function f(x) =(x2+5)2

Q: Togaritnmic difterenti ation f(X) = (4x3+1) (x? +5)3 to find derivative f'(x) = (20 Use %3D

A: f(x)=(4x3+1)(x2+5)3

Q: Plot the function f(x) = x3– 2x2– 10 sin?x - e0.9x and its derivative for -23x54 in one figure. Plot…

A: Given : fx=x3-2x2-10sin2x-e0.9x Differentiating wrt x , we get…

Q: point(s) on the graph of f where the tangent f(x) = %3D x² + 25 x-value (x, y) %3D

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Q: Using the First Derivative Test, what are the local extrema for the function g(x) - + 9x- 28x + 1?…

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Q: Determine the sign of the second derivative function as x varies. Where is f' positive? Where is…

A: According to question given thatf"(x)=-4(-3x2+1)(x2+1)3

Q: QI Find f'(x) for 1+ sec 1(x) f(x) = 1- csc-1(x)

A: Use quotient rule to derive the f'(x).

Q: uestion 4 .2 F(x)=f(x) and F(– 1) = F(2)= -5, then f(x)dx= -1 If

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Q: QI Find f'(x) for 1+ sec-(x) S(x) 1- csc-1(x)

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Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

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Q: Using the definition of a derivative, find f' (z) given f(x) = -r +4x +4x +2. (Do not include"f' (x)…

A: Given, fx = -x3+4x2+4x+2  We have to find the value of f'x