2. Let f(x) = x4 – 8x³ + 10. (a) Find the critical points of f. (b) On what intervals is f increasing? decreasing? Make it clear which answers are which, and justify your answer by including an appropriate sign chart as part of your work. (c) Find all local maximum and local minimum values of f, giving x and y coordinates with each answer. Make it clear which answers are which, and justify your answers with appropriate supporting work.

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A:

Q: Q2 (a) Let f (x) = x* - 4x³ + 10 (i) Find all critical points of f(x). Determine whether the…

A: For, critical points we take f'(x) =0 For, inflection points we take f''(x) =0

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A:

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A:

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A:

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A:

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A:

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A:

Q: Suppose that f ‘(x) is negative for x 1. Does f have a local minimum or maximum value at x = 1?

A: The answer is 'YES' Let see how it is YES in next step.

Q: Let f(x) = x3 – 6x2 + 1. a. Find the critical numbers for f.   b. Determine the intervals on which…

A:

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A:

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A:

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A: Let us use the golden section method to determine with an accuracy of 0.25 the minimum of the…

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A: f has a local minimum at x=0 and a local maximum at x=2.

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A: According to our policies we are allowed to solve one question at a time. Kindly repost other…

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A: Use derivative

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A: Given: fx=x2-4x+1 and x∈-3,3   The Power law: ddxxn=nxn-1

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A: Critical point and the absolute minimum is determined as shown below

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A: at x=-3 and x=5 f is relative maximum

Q: ,2 Let f(x) = x – 12x -27x + 1. Find the critical points of f(x).

A: Find the derivative as follows: f'x=ddxx3-12x2-27x+1        =3x2-24x-27

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A:

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A:

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A:

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A: Maximum minimum value problem....

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A:

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A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: snip

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A: If f'(x)=x3-2x2-x+2, then f has relative minimum at x

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A: Find f'(x) using exponent rule.

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A:

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A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.