Use the first derivative test to find the location of all local extrema for .3 f(x) = +4x*+7х— 5 3

Q: 7. Use the definition of the derivative (long method/ increment method) to find the derivative of…

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Q: Find the derivative of h(x)=(3x+4)3/  (−3x−2) 4 You should leave your answer in factored form. Do…

A: The given function is h(x) = (3x+4)3/(−3x − 2)4. Rewrite the given function as h(x) = (3x+4)3/(3x +…

Q: Use the second derivative test to find the extreme values of the function J () = x³ – su² 24X .

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Q: Find the derivative of the following functions by applying “Delta Method". Show your complete…

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Q: Use the derivative of the function shown below to determine the open intervals in which the function…

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Q: Q1) Find the Derivative to the function and find local minimum and local maximum points y = 3x? - 3

A: y=3x2-3 We need to find the derivative of the function and to find the local minimum and local…

Q: Some values of adifferentiable function f and its derivative are given below. 2. 4. 15 13 10 6.…

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Q: In x se the second derivative test to find the local extrema for the function f (x) = x3 •

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Q: 10. Iff(x) = Vx find f (4). 11. Use the limit definition to find the derivative of f(x) = x² –2 x.…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

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Q: b) f(x) = xe

A: If f(x) is a function of x and the second derivative of f(x) exist at any stationary point x0.1.If…

Q: Find the critical points of the following function. Use the Second Derivative test to determine (if…

A: Given: z=fx,yz=x2+10xy+y2-----------------------Aim: To find each critical points corresponding to…

Q: Q:2. Use the first derivative test to find the intervals on which the function is f(x) = x4. which…

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Q: Fill in each blank so that the resulting statement is true.

A: The slope of the tangent at a point on the curve is equal to the value of the derivative of the…

Q: Determine for what values of x the function f(x) = 32 ln(x) − x^2 + 6x − 5 has a tangent line with…

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Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

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Q: 2. Find the derivative of the following functions: (a). f(x) = x + 4x-2 + 6e" [1 Mark]

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Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

Q: Find the derivative of the following functions by applying "Delta Method". Show your complete…

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Q: 3. Use derivatives to find the critical points anc (a) f(x)= x³ – 9x2 + 24.x + 5

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: I. Find the derivative of the following. Show that the applicable differentiat rules has been used.…

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Q: : (#3) f(x) = x + #4) Given the function f(x) =x3 –x² + 2x - 1. Use the second derivative test,…

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Q: Find the anti-derivative of g (x)=−8ex+4 − 5/ x+7. (Do not include the constant C in your answer.)

A: We have to find the antiderivative of g(x) .g(x) is given by:

Q: Find the derivative: n[(x³ + 2) (x² + 3)]. Evaluate S dx. Зx8 — 2 2x*- x2 Evaluate dx.

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Q: 1.Use the second sufficient condition for an inflection point (the third derivative test) to find…

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Q: The first derivative of a continuous function y=f(x) is given, find y’’ and then sketch the general…

A: Our objective is to find y'', and then sketch the general shape of the graph of  f.

Q: Use the Generalized Power Rule to find the derivative of the function. y = (1/w^7-1)^6

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Q: Find the relative extrema of f(x) = 9 + 30x – 5x? using both first and second derivative tests. f(x)…

A: Derivative one time and equate it to zero to find the critical point. Derivative second to find the…

Q: Find the derivative of the function g(x)=x2∫0√1+t2dt.

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Q: Given the function f(x) = – x° – 6x2 + 5x + 12 , use either the First Derivative Test OR the %3D -…

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Q: 1. Use the Power Rule and properties of derivatives to find the derivative of each function a) f(x)…

A: Here we have to find the derivative by using power rule and the properties of the derivative.

Q: Find the critical points for the following function. Then use the second derivative test to…

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Q: b. Use the Second Derivative Test to find all local minima and local maxima for g(x).

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Q: 8. Find the derivative of the following functions with respect to x by using either the product or…

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Q: t(x)=23x3−10x2+42x+9 Given the function above, use the First Derivative Test to find the local…

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Q: Find the relative extrema of f(x) = 2+ 90r 5x using both first and second derivative tests. f(x) has…

A: We can find the relative extremum as below

Q: Q4. Find the slope of the tangent line to the function f(x)= e* +3; x+2 at x=4 5x-10

A: Given : fx = ex5x-10

Q: 4. Given f (x) =x' -12x +1. Use the second derivative test to determine the local extremum of f (x…

A: See the attachment.

Q: 6. Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x)

A: Slope of tangent is obtained by derivative of the function f(x).

Q: 2the second derivative test to find the loscal maxilnum and minimulin of thie functioni 3 f (x}こ 2メ2…

A: To find the local maxima and local minima of the below function. fx=2x3−3x2−12x

Q: Find any relative extrema. Where applicable, use the Second Derivative Test to verify. (a) f(x) = (x…

A: a)  f(x)= (x+9)2 b)   f(x)= x4 -2x2 +6 c)  f(x) = 2x +18/x          provided x≠0 To find relative…

Q: 3 Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x) =

A: on solving this we get the

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

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Q: Find all possible functions with the given derivative. 7) y' = 5x2 + 1 %3D

A: solution = y' = 5x2 + 1  y' = dy/dx dy/dx = 5x2 + 1 ∫dy = ∫(5x2 + 1 ) dx + c  [ yn dy = yn+1 ] y…

Q: Q/2: Find the derivative of the following: (a) y = (x²ln x)* (b) y = In 1-x

A: According to power rule of differentiation . According to product rule of differentiation .

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

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Q: C45 O Use the first derivative test to find the local extrema of f(x) where f(x) = 4x3 - 36x.

A: (A)- local maximum at - root(3) and minimum at root(3)

Q: 7. Use the limit definition of the derivative to find f'(x). Then find the equation of the tangent…

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