5. For the function h(x)= 3x - 20x + 7 a. Find the intervals on which h is increasing or decreasing. h is increasing on: h is decreasing on: b. Find any local maximum and minimum values using the Second Derivative Test.

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: A producer of pedal-powered ice cream makers has determined that the revenue from the production and…

A: Given: Rx = 46x- 0.04x2 , 0≤x≤900 To find the interval of increasing and decreasing, we have to find…

Q: A producer of pedal-powered ice cream makers has determined that the revenue from the production and…

A: Given Data: A producer of pedal-powered ice cream makers has determined that the revenue from the…

Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: 1. Consider the following function: f (x) 2x2 – x4 A. Find the critical values. B. Use the "Second…

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Q: b) For f(x) = x²/(4 – x²), find the intervals in which it is increasing/decreasing, Concave down/up,…

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Q: For the function f(x)=x^3−27x, its local maximum is __ which occurs at (___; its local minimum is __…

A: To find the local maximum and local minimum for the function f(x) = x3 – 27x

Q: 3. Given f(x) = x³ + x² – x + 1, on the interval bsolute maximum and minimum values, and indicate…

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Q: Given f(x) = x^3 - 27x + 5, list the interval (a,b) where f(x) is decreasing, AND at what x-value…

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Q: Given the following function,f (x)= -x^2-10x-25 , use the second derivative test to decide whether…

A: Now the equation(function) given in the question f(x)=-x2-10x-25

Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

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Q: Determine if the MVT applies to the function on the given interval. If so, find the points that are…

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Q: For the function f(x) = |x2 − 4|, find the critical points, test them to find extreme values. Which…

A: According to the given information, it is required to determine the extreme values of the function.

Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

A: f/x=x-12x+2 a). Critical points are the values of x for which first derivative is zero or not…

Q: 4. Use the linearization of the function f(x)%= at an appropriate x=a value to approximate 4.002

A: Given: The function f(x)=1x

Q: 2. Consider the following function; f (x) = x² /5 - A. Find the critical values of "f ". B. Use the…

A: The function is fx=x25-x

Q: For the function f(x) = x³ – 27x, its local maximum is which occurs at ( its local minimum is which…

A:

Q: The function f has a continuous second derivative, and it satisfies f(-6) = -1, f'(-6) = 0 and…

A: Maxima minima problem....

Q: For the following function: a - find all critical numbers b - find the open intervals over which the…

A:

Q: Find the slope of the line tangent to h(x) = f(x)g(x) at x = 6, given that the line tangent to the…

A: We have to find

Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

A: Maxima minima: ƒ'(x) = (x - 7)(x + 1)(x + 5) Critical points of f exist in those points where…

Q: For −10≤x≤14the function f is defined by f(x)=x^3(x+3)^4 On which two intervals is the function…

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Q: 1. Given the function f(x) = Vx5 – 3Vx², find the interval(s) of increase.

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Q: On the graph of f(x) = cos x and the interval [-2n, 0), for what value of x does f(x) achieve a…

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Q: )For the function f(x) = x-48x, its local maximum is which occurs at ( ... its local minimum is…

A: Solve by derivative test

Q: Given the function g(x) 6x – 27x2 – 72x, find the first derivative, g'(x). = (x),6 Notice that g'(x)…

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Q: We want to study the following function on the interval I = [-2; +[ %3D 3x? + 4x +3 g(x) : %3D x² +…

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Q: 4. Find the point on the graph of f(x) 5x2 + 20x – 3 where the tan gent line is horizontal. (a)…

A: We have to solve integration

Q: Use the limit formula for the derivative of a function at a point to find f'(-3) for f(r) = 2r2 – r.

A: use limit definition to find the value of derivative.

Q: For f'(x) = (x – 7)(x + 1)(x + 5), Find (i). What are critical points of function (ii). On which…

A: Given,            f'(x) = (x - 7) (x + 1) (x + 5)

Q: Given the following function: f(x) = x^2 lnx - Find the critical points for each of the functions…

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Q: For the function f(x)=6x+2sin(x)f(x)=6x+2sin⁡(x), find all intervals where the function is…

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Q: 9. Given the function f (x) = 3x -4x2 + 2, use the first and second derivative tests to find: a) the…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: The function f(x)=(1/(x+1))+4 is decreasing on what interval(s)?

A: Consider the function  fx=1x+1+4

Q: For the following function: a - find all critical numbers b - find the open intervals over which the…

A: Given f(x)= x2 +6x+10  We first find  all the critical number.

Q: find the value of the constant (a, b, or c) that makes the function continuous

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Q: Use the second derivative to determine the intervals on which the given function is concave up and…

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Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = V f(x), evaluate…

A: To find: The value of g'(4) if g(x)=f(x). Concept used: Chain rule: f(g(x)=f'(x)g'(x)

Q: 1. Use the second derivative test to find the relative extrema of the following function. f (x) =…

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Q: Make a graph of the functionƒ(x) , for x ≥ 1. Be sure to include all of the evidenceyou used to…

A: Given:  The function fx=∫1xdtt for x≥1, To sketch: The graph of fx for x≥1,

Q: For the function f (x) =x³ – 3 -x² + 8 , find the coordinates of all Critical Points.

A: Given, fx=x3-3x2+8

Q: Find the approximate value of the function f(x)=√5x−1 at x=1,99.

A: Given Here a = 2. The formula for approximate value is Substitute a = 2 in given function to get…

Q: On the graph of f ( x ) = sec ( x ) and the interval ( -2π, 0 ], for what value(s) of x does f ( x )…

A: f(x) = 1 on, (-2π, 0] Implies, sec(x) = 1 on (-2π, 0] i.e. x = 0 on (-2π, 0] So, x = 0  The graph of…

Q: On what interval(s) is the function -9x3 g(x) = e both decreasing and concave down?

A: The interval in which the given function g(x) is both increasing and concave down must satisfy the…

Q: 5. Find the length of the curve given by the graph of the function f(x) = x/x, for a in [1,4].…

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Q: 3. Given the function g(x) = x - 2x2 + x, find the interval(s) when g is concave up and decreasing…

A: We have given a function g(x).  We have to find the interval where g is concave up and decreasing at…

Q: Find a value for the constant k, if possible, that will make the function continuous. kox+1 for x 3

A: K = 1/3

Q: 1. Consider the following function; f (x) = 6x A. Find the critical values of "f ". B. Use the…

A: As per our guidelines we are allowed to solve 3 subparts of a multipart question at a time. Kindly…

Q: Show that a function f decreases most rapidly at x in the direction opposite to the gradier (that…

A: Solve with given conditions

Q: For the following functions, find all the critical values, identify intervals of increase and…

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