a) Determine the intervals that the function F(x) - х - 3x - 24х It is increasing and decreasing b) Using the first derivative criterion, find the graphs of the function F(x) = x³ – 6x²+ 9x + 4

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function is fx=x6-x3. a. Find the absolute extremum using the first derivative test. b.…

Q: Let f(x) = x² – 8x – 14 Use the second derivative test to find any local maxima and minima. First,…

A: for critical value put first derivative zero if second derivative positive minima and if negative…

Q: Perform a first derivative test on the function ​f(x)=2x3 +3x2 −12x +4​;​[−2​,4​].   a.  b.Use the…

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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: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Consider the given function as fx=x-33x+4. The limit definition of the derivative of a function fx…

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: Given function is fx=x2-6x+5. Critical numbers of a function is the point where its first derivative…

Q: 4. Use the first derivative test to find the intervals of increase and decrease, and the relative…

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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: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: f(x)=(x-1)2(x+3) To find out critical numbers , we take derivative and set it =0 apply product rule…

Q: Consider the function h(x) = 2 - 4x2 + 10. Use the second derivative test to find the r-coordinates…

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Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: Derivative of a function determines the change of a variable with respect to another variable. First…

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| f'(x)= ?

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 the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

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Q: 2. a) Find and fully factorise the derivative of f(x) = (2x + 1)2 using expansion and the power…

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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: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: f(x)=x2+6x+10

Q: a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and…

A: Given ƒ(x) = 2x3 + 3x2 - 12x + 1 on ⌊-2, 4⌋ (a) Find the critical points first dfdx=6x2+6x-12 Put…

Q: Given the function g(x)=8x3-12x2-288x, find the first derivative, g′(x). g′(x)= Notice that g′(x)=0…

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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: 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: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

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Q: Find an equation of the tangent line to the graph of the following function f at the specified…

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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: Given the function g(x) = 8x + 96x + 360x, find the first derivative, g'(x). %3D = (x),6 %3D Notice…

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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: (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is…

A: f(x)=(8-x)(x+1)2

Q: 1.Use the second sufficient condition for an inflection point (the third derivative test) to find…

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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: 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: f (x) = x² – 3x/3 [0,2]

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Q: a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and…

A: the given function is: f(x)=-x3+9x the given interval is [-4,3] (a) we have to locate the critical…

Q: For the function, find all critical numbers and then use the second-derivative test to determine…

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Q: a)Use the second derivative test to determine whether the function has a local maximum or local…

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

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Q: Find the derivative of the function f(x) = 4x2 – 13x – 30 by definition of derivatives f(x + h) –…

A: We have to find the derivative of the given function: fx=4x2-13x-30 by the definition of…

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

A: Please refer the attached image for complete solution.

Q: Consider the function y = -x3 + 3x² – 2. a) Find the critical points. b) Use the 2nd Derivative Test…

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Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and…

A: Given fx=x4-x2 on -2, 2

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

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Q: Find all critical numbers for the following function. Then use the second-derivative test on each…

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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: How did the function f(x) = -x^3 + e^x - 8 satisfy the intermediate value theorem? Show that f has a…

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Q: Given the function g(x) 623 9x2 360z, find the first derivative, g' (x). %3D %3D = (2),6 Notice that…

A: Follow the procedure given below.

Q: Find an equation of the tangent line to the graph of the following function f at the specified…

A: The given function is f(x)=4xx2-5. Find the equation of the tangent line to the graph of f(x)=4xx2-5…

Q: Consider the function h(x) = ((x^2) - x) / ((x + 1)^2), which has first derivative h'(x) = (3x - 1)…

A: To find the vertical asymptotes, locate and classify all relative minima and maxima and point(s) of…

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

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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…

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