Consider the following function. f(x) = x* + 4x3 + 11 (a) Make a sign diagram for the first derivative. --Select- -Select- -Select- -Select- -Select--- f'(x) > 0 f'(x) < 0 f'(x) = 0 undefined (b) Fam for the second derivative. -Select-- --Select-- --Select- --Select-- Select-- (c) Sketch the graph, showing all relative extreme points and inflection points. y 15 15 10 10 IP IP 5 5 4 -5 -5- IP -10 IP -10 -15 -15 2. 2.

Q: Find the higher order derivative  f'(x)=7x2-9x2+4x f'''(x)=

A: We will use the following : ddxxn = nxn-1 ddxc = 0 where c is constant.

Q: 13. f (x) = sinx3 (2х-1)2

A: I have stated the used formulas in the solution

Q: Find the derivative of f(x) = 2x²+3x-1 if f'(-1)

A: Given: fx=2x2+3x-1

Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

A:

Q: 8. Find the derivative of f (x) = 2tanx – 3secx. Show all steps -

A: We have to find the derivative of the function fx=2tanx-3secx Then,…

Q: 2. If the derivative of an accurately determined function is replaced with a finite difference, how…

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

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Q: 2. Find the derivative of f'(x) if ƒ(x) = x*+3x-V x2+x

A:

Q: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2   As we know that; To calculate the critical point, f'x=0.

Q: What is the second derivative of f(x) 2x-3 2 x+1 10 (x+1)* 10 3 (x+1)° -10x+10 (x+1)* 10x-10 (x+1)*

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Q: Determine the derivative of y = ln(4x² - 2x). O 8x-2 4x-1 8x-2 4x²-x 4x-1 4x²-x 4x-1 2x2- -x O O

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Q: 1.f(0) = (금x* + 3)" %3D

A:

Q: Find the derivative of the function using Chain Rule. (2x-6)-¹ (x²+3) h(x)=

A:

Q: find the derivative of the function F(x)=4(x^3-x)^4

A: According to the given information, it is required to find the derivative of the given function.

Q: If the derivative of f is f'(x) = (x – 1)(x + 2), then f is decreasing on (-2, 1) Select one: True…

A:

Q: 5, i, Evaluate the first and second derivatives of the function z-2x4+3x3+2x-5 when x = 4.

A: We have to find the first and second derivative of the function z=2x4+3x3+2x-5 when x=4.

Q: Find the derivative of f(x) = (6x² + 6x – 4)arctan x - 1 (бх? + 6х — 4)arctan x(- In(6x2 + 6x – 4) +…

A: Given function is  y=6x2+6x-4arctan x Taking log to each side, we get lny=ln6x2+6x-4arctan x   We…

Q: Find the derivative of the function. (x) - In(4 - x") f'(x) -

A: Find the derivative of the function.      fx=ln4-x8

Q: Find the derivative of the function. 4 - 4x – x2 f(x) x2 - 6 — 4х — 2 - -1+ f'(x) = -x – 6

A:

Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

A: 1.f(x)=(2x2-2x+1)3 2. f(x)=5x3-8x2+9x-6

Q: Compute the derivative of f(x)= (ex2 +e-x2 )/(ex2 -e-x2 )

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Q: The second derivative of a function is equal to 1. If the graph of the function passes through (0,2)…

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Q: Example 4:- By using the four steps rule, find the derivative of the function f(x) = Vx + 2

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Q: Find the relative extrema of the function f(x)= x2+3x+4 using first derivative test.

A: fx=x2+3x+4 To find extrema of function.

Q: Find the derivative of f(x) = 6* – 3* + In x -

A: Differentiate: fx=6x-3x+lnx

Q: Find the derivative of the function by the limit process. f(x) = 7x − 3

A: GIven function: f(x) = 7x − 3 Formula used:

Q: 3. Find the derivative of f(x) = x2020 – 2019.x" – 7x3 – 9x + en".

A: To Determine: Find the derivative of f(x)

Q: Find the derivative of f (x) = -4 tan (x).

A:

Q: f(x) =  3 − 3x − x2 x2 − 5  f '(x) =

A:

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.

Q: 3 Determine the 3rd derivative of the function f(x) = 2√√x-x³

A:

Q: Find the derivative of the function by the limit process. 7 f(x): x - 9

A: Given,          The function is fx=7x-9.

Q: What is the second derivative of f(x)=−x4? at the point x=−3 Do not include "f′′(x)=" in your…

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Q: Find the derivative of the function using Chain Rule. Given f(x)=(x²+x-3)√√x²+x-3

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Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6)…

A: Product rule (u v )' = u ' v + u v' Formula derivative of xn=n xn-1 Derivative of arctan…

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: Estimate the derivative of the function f (x) = - 3 at the point x = 3. 5 5

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Q: equation of the function f whose graph passes thro f'(x) = x/25 - x²

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Q: he first derivative of f(x) = ln(5X4 - 6x) will be

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Q: If a function is increasing everywhere (and it has a derivative), then it's derivative function is…

A: explanation of above question is given below,

Q: Find the function with the given derivative whose graph passes through point P. F'(x)=2x-3, P(5,5)

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Q: 2) Find the derivative of the function f(x) = 3x² by definition

A:

Q: Find the indicated derivative. f'(-5) = If f(x) = x², find f'(-5). X

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Q: (x² +2)S UI -人 S-X

A: →First of all, simplify the given expression using logarithmic property.              ln(ab) = ln(a)…

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: Find the derivative of f(x) = arctan x In(6x² + 6x – 4) 1 1 arctan x 6x2+6x-4

A: Here the given function fx=tan-1x ln6x2+6x-4

Q: The first derivative of the function f(x) is given by its graph.. f'(x) 3- 2-

A: A.  Function is increasing when f'(x) &gt; 0  from graph  Function is increasing…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.