The function f(x) = 6x + 8x has one local minimum and one local maximum. Algebraically use the derivative to answer the questions: (Leave answers in 4 decimal places when appropriate) this function has a local maximum at x = with value and a local minimum at x = with value

Q: 1. Find derivative of given function defined as follows. 7-29-22 y = (8x²-3x³) ³

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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 value of the derivative (if it exists) at the indicated extremum. -4 4/6 3 f(x) = - 3xVx +…

A: To find: The value of the derivative fx=-3xx+2. Formula used: Product rule of differentiation:…

Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (x) = 5x – 4

A: Note:- These are multiple questions and according to our company guideline we can do maximum 1…

Q: Given the function g(x) = 8x³ + 12x² – 48x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

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Q: Q1/a- Write an equation of the Line that passes through point: P1 (-2,0), P:(2,-2)? b- find any locl…

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

A: We have to determine the relative extreme values of the function using the first derivative test.

Q: Suppose a tour guide has a bus that holds a maximum of 110 people. Assume his profit (in dollars)…

A: Given : Profit function P(n) = n(55-0.5n) - 110 Maximum value of n = 110.   To find : a. How many…

Q: Determine the critical points of f(x) = x^2+8x+ 10 and apply the Second Derivative Test to find the…

A: Critical points are points where the function is defined and its derivative is zero or…

Q: Given the function g(x) = 8x – 84x? + 240x, find the first derivative, g'(x). = (x),6 Notice that…

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

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Q: Given the function g(x) = 8x* + 84x² + 288x, find the first derivative, g'(x). = (x),6 Notice that…

A: Since, you have ask multiple part's in the question. I am answering for first three parts. Please…

Q: Find the x-coordinates of all local maxima using the second derivative test. g(x) = 2° – 3x7 +2

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

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Q: Find the derivatives of the function f(x) from the first principle x4+4

A: Here is the solution

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

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Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: given,        fx=1-2x4x+5

Q: Find the derivative.

A: Differentiate above equation with respect to x dydx=ddx{ln(x+1x3+1)}dydx=1(x+1x3+1)ddx(x+1x3+1)…

Q: Find the derivative of function defined as follows. y = 5x-5 - 6x-2 + 13x-1

A: Given function is: y=5x-5-6x-2+13x-1 We have to find dydx. We will use the following formula for…

Q: Find the derivative of the function.

A: Given function is Differentiating both sides with respect to x, by using product rule of…

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

A: Given function, gx=x2x2+3

Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

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: Given the function g(x) = 4x° + 30x2 + 48x, find the first derivative, g'(x). gʻ(x) = Notice that…

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Q: Find the derivative of function defined as follows. y = (x3 + 2)(x2 - 1)4

A: Given: The function y=x3+2x2-14, To determine: The derivative of the given function.

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: Two business students at Brock University decided to open a small company together to sell their own…

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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: (B) Use the first derivative test to find the maxima and minima for f(x) = 3. 5z2 + 6x +9. 2.

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Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: find a linearization at a suitably chosen integer near a.

Q: Find the value of x for which the derivative is zero of Y =x +4x - 3x – 5

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Q: Given the function g(x) = 4x° + 36x + 60x, find the first derivative, g' (x). %3D = (2),6 Notice…

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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: 1. Use the definition of derivative to find the derivative of (a) f(x) = (x + 1)² 1 (b) f(x) =…

A: The solution are next step

Q: 5. f(x) = [(x + 5)5 – 1]4

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Q: 1) find the derivative of y = 4x2 – 3x – 2 | | then evaluate f'(x+3)

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Q: Given the function g(x) = 8x° + 12x2 – 480x, find the first derivative, g' (x). g'(x) = Notice that…

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Q: 11. Use the definition of the derivative to find f'(x) for the function f(x) = x2 + x + 2. Show your…

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

Q: A graph of yY = f(x) is shown. In the same coordinate system, sketch a graph of the derivative func…

A: when a line passes through two given points, say (x1, y1) and (x2, y2).  the equation for this line…

Q: Consider the following function. g(x) = x2 - 2x - 6 on [0, 8] Find the derivative of the function. 9…

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Q: What is the derivative of f(x) = -3? Do not include "f'(æ) =" in your answer. For example, if you…

A: Given            f(x)=-3

Q: 8. Find the derivative of the function f(x) = x ² - 10x + 3 using First Principles.

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Q: Suppose the first derivative of a function is f'(x) = (x- 30)(19x+ 1). The function f is decreasing…

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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: Find a function with the given derivative whose graph passes through point P f'(x)=x-4, p(1,7)

A: Integrating on both sides, we get

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