Use the first derivative test to locate all local extrema for 3 f (x) = -x'+ = -x' +- x +18x.

Q: What is the first derivative of s(x)=(7x)3x at x=4?

A: To evaluate s'(4)

Q: Find the derivative of f(x) = tan tan (3x2+2x)( Ans: (6x + 2) sec2 (3x2+2x) solution?

A: Let,

Q: Find the derivatives of the functions in Exercis y = xe-x + ex3

A: y=xe-x+ex3

Q: Apply the second derivative test to find all relative extrema. - 5)² (a) f(x)=(x

A:

Q: Find all relative extrema of the function f(x) = x* – 4x2 + 2 by using the Second Derivative Test…

A: Given, The function  fx=x4-4x2+2 We have to find the all relative extrema of the function using the…

Q: f(x)= xe* In(x³)

A: f(x)=xe-xln(x3)According to question we have to calculate the derivative of the function.

Q: Find the derivative of ¤(x) at x = /3/2 where rsin-'(x) $(x) = eº tan 0 do. x2

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Q: Find all relative extrema of the function f(x) = x* – 4r +2 by using | the Second Derivative Test…

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Q: Apply the second derivative test to find all relative extrema. (c) f(x) = 1

A: To find the relative extrema first we  find the critical points. The critical points are the values…

Q: show that nth derivative of  f(x)=x^2/(2x+1)(2x+3)

A: nth derivative of f(x)=x2(2x+1)(2x+3) f(x) can be written as by using synthetic division method…

Q: 13. f(x) = e* In x

A:

Q: Use the first derivative test to find and classify the relative extrema of x2 +8x+ 16 f(1) = For…

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Q: Estimate the derivative of f(x) = sin x at x = π/6.

A: Given,       f(x) = sin x at x=π6

Q: Apply the first derivative test to indentify all relative extrema. f(x) = cos² (2x)

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Q: 2.Find the derivative of y = In cosh x. %3D

A: Using chain rule of differentiation.

Q: Find the derivative ofƒ(x) = 1/x5in two different ways:using the Power Rule and using theQuotient…

A: given: f(x)=1x5 the differentiation of the function f(x)=1x5 by using the power rule is: the…

Q: Find the 139th derivative of y=cos x а. Cos x b. Sin x С. -Cos x d. -Sin x

A:

Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

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Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

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Q: Use the First Derivative Test to find the relative extrema of x – 3 f(x) ex

A: The given function is fx=x-3ex. We need to find the realtive extrema. Concept used:  Consider x=c is…

Q: fcx)= Y文 メ ー^

A: Local extrema

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: Estimate the derivative of f(x) = sinx at x = π/6

A: Since,it is known that the derivative of the function with any variable measures the rate of change…

Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

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Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) %3D f (x) =

A:

Q: Find the derivative of the function. y = arctan 1 + x 1 - X y' =

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Q: what is the derivative of f(x)=ln(tanhx)

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Q: What is the derivative of f(x)=2sin(x) at the point x=−π/2?

A: To find the derivative of fx=2 sinx, at the point x=-π2.

Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: Find the derivative 4 y = In x +

A: It is given that- y=lnx+4x To find the derivative of y, use the addition rule, i.e.,…

Q: Find the relative extrema of f(x) = 4+70x – 5x² using both first and second derivative tests. f (x)…

A: Given:- f(x) =4+70x-5x2  To find:- Relative extrema of f(x) using both first and second derivative…

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 4 using a value…

A: Given function is y=tanx. We have to find the first derivative of y=tanx at x=π4 using a value of…

Q: Can the  derivative of f(x) be zero in the interval [-1,0]

A: Given, fx = x4+8x+3  f'x = 4x3+3   We have to find the derivative of fx be zero in the interval -1,0…

Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: find implicit derivative dy/dx of x2sin2(y)+2x2=y

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Q: f(x)= sinx/cos x+1

A:

Q: Use the first derivative test to identify all relative extrema  f(x)= 1/2x-sinx on the interval…

A: Maxima or minima: If f(x) is any function: 1) Evaluate f'(x)=0 for critical point. 2) Evaluate…

Q: Find the derivative of f ( x ) = 6 sin ^2 ⁡( x ) + 6 cos^2 ⁡( x ) at x = -6.5

A:

Q: Use the second derivative test to find all relative extrema  f(x)= x+4/x

A: The given function is as - f(x) = x+4xProcedure to find local extremas - 1. Find f'(x)2. Put f'(x) =…

Q: Calculate the derivative of the function y=arccos x arctan x at x=0.

A: Differentiating with respect to x, we get

Q: By using first principle, show that the derivative of f(x)=- is x+1 1 S'(x) = (x+1)

A:

Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) f'(x) =

A: Given problem is :

Q: Find the derivative. Simplify where possible. y  = x tanh-1 x   + In √ (1- x2)

A: We have given that, y=xtanh-1x+ln1-x2 We have to find the Derivative of this function i.e. y' As we…

Q: Find the derivative car (x+y) = yrinx

A:

Q: Find the derivative. f(x) = eX cosh(x) f'(x) =

A: First use relationship between hyperbolic function and exponential function convert coshx in…

Q: Find the derivative. f(x) = tanh(2 + e4x) f '(x)

A: