Suppose the function g(x) has a domain of all real numbers except x --9. The second derivative of g(x) Is shown below. (x-4)(x + 5) (x + 9)3 g "(x) = a) Give the intervals where g(x) is concave up. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) b) Give the intervals where g(x) is concave down. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) c) Find the x-coordinates of the inflection points for g(x) . (Enter your answers as a comma-separated list. If an answer does not exist, en

Q: Find all relative extrema of the function f(x) = x4 - 4x2 + 2 by using the Second Derivative.

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Q: Find the derivative of the function.

A: Use the chain and quotient rule of derivative to differentiate the function.

Q: Q1 Prove that the derivative of (2x +1) 2 is 4 (2x + 1) by using first principle derivative.

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: By the fundamental theorem of calculus if we have F(x)=∫f(x)dx then F'(x)=f(x). In some cases an…

Q: - Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

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Q: Find the derivative of: f(x) = (x3 + 2) In(x)

A: Consider the function

Q: The derivative of (x3 - 4x)>x is obviously 2x for x  0, because (x3 - 4x)>x = x2 - 4 for x …

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Q: Suppose the derivative of a function  f isf'(x) = (x+ 1) 2 (x -3)5 (x -6)4. On what interval f  is…

A: f(x) will be increasing if f'(x)>0    We first find the zeros of f'(x) They are x=-1 , 3, 6

Q: 5. Use the definition of derivatives to find f'(2) given that f(x) = 2x² -r+1

A: According to our company guidelines we are supposed to answer only one question since you have asked…

Q: Find q′(x) from q(x)=−5x3+x2−3x−3 using the definition of a derivative. (Do not include "q′(x)=" in…

A: Express the mathematical expression for the definition of derivative. f'(x)=Lth→0f(x+h)-f(x)h Given…

Q: For k(x)=(x−1)(−x2−2x)(2x−2), find the derivative of k(x) using the product rule. Do not include…

A: Obtain the derivative of the function k(x) as follows.

Q: If the derivative of f(x) evaluated at x=-2 es 122 y f(x) = ax^3 -3x^2 + 2x -5 and then the value of…

A: Using derivatives & given values.

Q: Use the Second Derivative Test to find the Maximum and Minimum value(s) of the function 3 f(x) x* -…

A: We have the given function as fx=32x2-4x+lnx For maxima/minima, we need to calculate f'x as…

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: 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: The derivative of the function f is defined by f'(x) = x² - 3 sin (x - 5). What is the x-coordinate…

A: How to find absolute minima of function f(x) in a given closed interval: find the critical points…

Q: 15. If f(x) = x2 - 6x - 9, find f(x) by using the formula/limit definition of derivative.

A: Given: fx=x2-6x-9 we know that derivative for any given functionfx by using limit definition is…

Q: Let f(x) = 2x ^ 3 – 7x + 3x ^ 7 – 2. Find the 4th order derivative evaluated at x=2. A

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Q: Find the equation of the tangent line to the graph of g(x) = f'(x) at x = -1 when f(x) = 5x³ + 2x² +…

A: Here, f(x)=5x3+2x2+2x

Q: Where does the derivative of g(x)=(x^2)/((x^2)+3) = 0 or is undefined?

A: Given function, gx=x2x2+3

Q: The first derivative of the function h is given by h' (x) = x³ – 3x2 + x. What are all intervals om…

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Q: Suppose the derivative of the function y​f(x) is (x-1)^2(x-5)(x-2). At what​ points, if​ any, does…

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Q: Find the derivative of the function. f(x) = 5x2 + 4x + 5 O 5x + 4 O 10x2 + 4x O 10x O 10x + 4

A: Given f(x)= 5x^2+4x+5

Q: Determine the value of X on which the derivative of the function Y = | 3x² + 4x + 1] does not exist.

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Q: Find the derivative of the function f(x) = (3x4-22³ - 10) ³/2 ○ f'(x) = (12x³ – 6x²)° ƒ' (x) = -—-…

A: The given function is f(x)=(3x4-2x3-10)32 We have to find the derivative of the function

Q: Show with the middle value theorem that the second derivative f'′ has at least one zero (for this…

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Q: Suppose 8 (x) =Vx+1,What is the correct result of the second derivative of g with respect to x? %3D…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: find the function with the given derivative whosegraph passes through the point P. g'(x) = 1/x2 +…

A: g'(x)=1x2+2x,P(-1,1) Formula ∫xndx=xn+1n+1+C

Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

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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 and state the domain of f(x) = In(x + 4) %3D

A: In this question, concept of derivative is used. Derivative The derivative expresses the rate of…

Q: (b) Find the derivative of f (x) = (x² + 2) (8x − 5) by using the product rule. Let g (x) = x² + 2…

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Q: f(x) = 2x²-4x x²+1

A: Given :fx=2x2-4xx2+1

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. 4 20) f(x) = 4 2 ,find f'(x) + 4 10 2 B) - x3/2 x2 x4 4 10 A) x1/2 x2 x6 4 10 4…

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Q: Determine the value of X on which the derivative of the function y 3x2 + 4x + 1| does not exist.

A: Giveny=|3x2+4x+1|y=|3x2+3x+x+1|y=|3x(x+1)+x+1|y=|(3x+1)(x+1)|Using modulus propertyy=|3x+1||x+1|

Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

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Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

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Q: Find the derivative of f(x) = (5x 2 + 3x + 1) × (3x 2 + 2x − 1) × (x 2 − 1). Show all steps.

A: Given:f(x)=5x2+3x+13x2+2x-1x2-1

Q: In(&x³) f(x) = 1-9e-* -2x 1-9e 2

A: Topic- derivative

Q: 1. Determine the derivative of: f (x) = 4x3 – x² + 5x + 9 %3D -

A: We need to find the derivative of the given function.

Q: Find derivative of q=(X^2-x+1)/x+1

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Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

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Q: If f(x)=2+ x-3 for all x, then the value of the derivative f'(x) at x 3 is

A: Given, f(x)=2+x-3

Q: 2. Use the definition of the derivative to find f'(7) if f(x) = 4 + 3x – 2x.

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Q: Find the derivative of y with respect to x. y = In(x - 4) 4 -x X-4 x+4

A: The given function is  y= ln(x-4)  We have to find the derivative of y w.r.t. x

Q: ***** Find the derivative of the function. Express the 2+3 f(x) 4- x2

A: The function is in the form of u/v. Kindly follow the attached imaged.

Q: 3. If f(x) = 2x² + 3x find f'(a) by using definition of derivative at a point a=4

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Q: What rule should be used in getting the derivative of a.)y = x^8 + 2x^6 - x^3 - 4x  b.)…

A: a) y=x8+2x6-x3-4xb) y=2x5+x-3x3c) f(x)=1-2x2