Consider the following function. f(x) = x3 + 3x2 - 24x + 6 (a) Make a sign diagram for the first derivative. --Select--- f '(x) > 0 v f (x) > 0 f (x) < 0 f'(x) = 0 f (x) = 0 f'(x) < 0 f (x) = 0 X = X = undefined (b) Make a sign diagram for the second derivative. f "(x) < 0 f "(x) = 0 f "(x) > 0 X = (c) Sketch the graph, showing all relative extreme points and inflection points.

Q: y = In (x* + 5)³

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Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x

A: Given Data: Function: fx=x3+2xlnx The product rule of derivative is, ddxfx·gx=fxddxgx+gxddxfx Use…

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Q: Find the derivative of ƒ (x) = 5ª In (x).

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Q: 1. Find the first derivative by using the definition for f(x) = 3x² – 2x – 5, hence - find f'(-2)

A: Derivative of a function is ratio of difference in output and difference in input.

Q: Can you help me with this problem step by step?

A: The equation is given by

Q: 8. Find the derivative of f(x) = (1+x³)' ( 14x + - ) using differentiation rules.

A: topic - derivative of a function

Q: Find the second derivative of the function.

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Q: 14) Find the first derivative of f(x)= 2*2*

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A: We have to find the derivative at that point

Q: 2. Find the derivative of g(x) = 2x sin x.

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Q: (b) Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y3. dx

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Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

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Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

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

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Q: Find the first derivative of the function of f(x) using any method?

A: Given,

Q: If f(x) = x³ + find f"(-1).

A: Since you have asked multiple questions in single request.so we will answering only first question.

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Q: Find the function ƒ(x) whose derivative is sin x and whose graph passes through the point (0, 2).

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Q: Calculate the first derivatives of ƒ(x) = x2/(x2 + 1) and g(x) = -1/(x2 + 1). What can you conclude…

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Q: Find the first derivative of ƒ(x) = 7x¹⁰² cot(x). 10 f'(x) =

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Q: 1) Find the second derivative of f (x) = 24 . %3D

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Q: Find the derivztive of the function

A: Topic :- derivative

Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

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A: we have to find the function f(x) whose derivative is sinx and whose graph passes through the point…

Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

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Q: function

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Q: Find the value of the derivative of the function f (x) = 16 - |x| at the extremum point ( 0, 16)

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Q: Find the derivative of the function. f(x) = (2x2 − x)ln x   f'(x)=

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