The function h(x) : 1 can be expressed in the form f(g(æ)) where g(x) = (a +6) and f(x) is defined as: f(x)=

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

A: Now differentiating with respect to x, we get

Q: Using the criterion of the first and second derivatives, find the graph of the function c) F(x) = x…

A: Topic = Functions

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

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Q: Find the derivative of the function f(x) = -8x² – 18x + 23 by definition of derivatives f(x + h) –…

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Q: use the Chain Rule to find the derivative. y = (x4 − x3 − 1)2/3

A: y = (x4 − x3 − 1)2/3 derivative formula ddxxn=nxn-1

Q: Find the derivative of the function using the power rule. (a) f(x) = 3/5x5 − 4x −4/3x-3 (b) f(x) =…

A: a) f(x)=35x5-4x-43x-3 f'(x)=ddx35x5-4x-43x-3       =35ddx1x5-4ddxx-43ddx1x-3…

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

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Q: The function f has a continuous second derivative, and it satisfies f(-8) = 5,f'(-8) = 0 and f"(-8)…

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Q: Find the derivative of the algebraic functie c3 – x³ c3 + x3 c is a constant. f(x) %3D 6r3 3 (3 +x³)…

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Q: Find the derivative of the algebraic function. f(x) = (x2 + 5x + 6)/(x2 − 4)

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Q: Find the derivative of the function. g(x) = 2(3 - 8x) g'(x)=

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Q: Using the criterion of the first and second derivatives, find the graph of the function a) F(x) = x³…

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Q: Find the derivative of the function. g (x) = 6x-3 + 2x Og (x) = 18x + 10x-6 %3D Og (x) = -18x-3…

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Q: For the function f (x) = 2x° – 3x2 – 12x, use the First Derivative Test to find the location of any…

A: The given function is- fx=2x3-3x2-12x To find the critical points of a function- dfdx=0…

Q: Find the derivative of the function. g(x) = [2 + (x² + 1)41³ g'(x) = 2 + (x8+ 4x6 + 6x² + 4x²+3)3

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

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Q: Use derivatives to sketch the graph of f(x) = (x² – 8x + 16)e².

A: Given

Q: A8: By use of the chain rule, differentiate the function f(x) = In(x* + 1).

A: It is differentiation using chain rule.

Q: Find the derivative of the function f(x) = 3x2- 13x 25 by definition of derivatives f(x + h) - f(x)…

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: 1. Use the limit definition of the derivative to find g'(x) if g(x) = 2x² – 6x + 13.

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Q: Find the absolute maximum and minimum, if either exists, for f(x) = x - 8x + 9. Find the first…

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Q: Find f' (x) using the rules for finding derivatives 4x2 – 7x +1 f(x): 2x + 9 f'(x)=O

A: To find The derivative of f(x)

Q: Find f'(x) using the rules for finding derivatives 5x2 - 9x +2 f(x) = 7x + 1 f'(x) =|

A: The given function is  f(x) = (5x2 - 9x + 2)/(7x + 1)

Q: Find the derivative of the function. g(x) = (1 + 5x)5(4 + x – x²)7 - g'(x)

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

A: A Function f has a local maximum at a point x0 if the values f(x) of f for x 'near'x0 are all less…

Q: Find the derivative f'(x) = f(x) = of the function. 2 - 58 - x x²-6

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Q: Use the Chain Rule to find the derivative. f(x) = (x5 – x3 – 1)2/5 %3D

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Q: Use the first derivative test to determine the relative extreme values of the function. below. a.…

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Q: Apply the definition of the derivative of a function to find f'(x). a. f(x) = 6x + 4 b. f(x) = x2 -…

A: To find the derivative of the function using the definition of the derivative. (a). Given function…

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

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Q: Let f(x) be a polynomial and g(x) = f '(x) be its derivative. If the degree of (f(x) + f(-x)) is 10,…

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Q: Find f'(x) using the rules for finding derivatives 4x2 - 7x +6 f(x) = 2x + 1

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Q: Find f (x) using the rules for finding derivatives 4x f(x) = -7x+ 1 %3D 3x +2 f'(x) =

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Q: The derivative of is f (x) = 3x* + 7x² + 5x + 2 %3D

A: Given, f(x) = 3x4 +7x2 +5x +2

Q: find the derivative of g(x) = (x+5)/(5-2X) using the definition of the derivative. must show all…

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Q: Find the derivative of the function f ( x ) = x2−10x+3 using First Principles.

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Q: Consider the function f(x) = i + x². How does this function essentially behave for large positive…

A: The Given Function f(x) contains rational function x/(x2+1) and polynomial function function…

Q: the derivative of the function g(x) In(lx2 +21)

A: We have to find the derivative of g(x)=ln(|x2+2|)

Q: Find the derivative of the function. g(x) = 4x2 + 7x3 g'(x) = %3D

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Q: Using the second derivative criterion, find the graphs of the functions b) F(x) = x³/3 - 9x + 3

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Q: Find the first and second derivatives of the function. g(x) = -4x3 + 11x2 + 6x - 51 g'(x) g"(x)

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

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Q: Rewrite the function g(x) = ((x^2)-1)/((x^2)+2) so that you can solve for the derivative using the…

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Q: Find the derivative of the function f(x) 3x2 – 12x by the definition of derivatives f(x + h) – f(x)…

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Q: 3x2 – x +1 - Find the derivative f'(x) by hand when f(x) %3D 2x + 7

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Q: Find the derivative of the function. g(x) = 2(3 - 8x)

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Q: x² +5x +6 f(x) = x² - 4

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Q: Find the derivative of the function f(r) = 3x² – 12x by the definition of derivatives | f(x +h) -…

A: here option C is true 6x-12

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.