Megan M.

asked • 05/03/16# Derivatives & the Shapes of Graphs

1. Answer the questions below based on the following information about the function f . You must justify your

answers.

(i) The function f is continuous and differentiable for all values of x.

(ii) f(x) < 0 for x < 0; f(x) > 0 for 0 < x.

(iii) f'(x) < 0 for −6 < x < −2 and 5 < x.

(iv) f'(x) > 0 for x < −6 and −2 < x < 5.

(v) f''(x) < 0 for x < −4 and 3 < x < 7.

(vi) f''(x) > 0 for −4 < x < 3 and 7 < x

answers.

(i) The function f is continuous and differentiable for all values of x.

(ii) f(x) < 0 for x < 0; f(x) > 0 for 0 < x.

(iii) f'(x) < 0 for −6 < x < −2 and 5 < x.

(iv) f'(x) > 0 for x < −6 and −2 < x < 5.

(v) f''(x) < 0 for x < −4 and 3 < x < 7.

(vi) f''(x) > 0 for −4 < x < 3 and 7 < x

(a) On which intervals is the function decreasing?

(b) What is the x-coordinate of each local maximum (if any)?

(c) On which intervals is the function concave up?

(d) What is the x-coordinate of each inflection point (if any)?

(b) What is the x-coordinate of each local maximum (if any)?

(c) On which intervals is the function concave up?

(d) What is the x-coordinate of each inflection point (if any)?

Would someone be able to explain this to me?

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## 1 Expert Answer

John R. answered • 05/03/16

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Financial professional with MBA/CPA looking for tutoring

A function is decreasing where its first derivative is negative; increasing where its first derivative is positive.

A local max occurs when the first derivative changes from positive to negative; a local min when it changes from negative to positive.

A function is concave up where its second derivative is positive; concave down where its second derivative is negative.

An inflection point occurs where the function changes concavity.

Hopefully this info will allow you to solve the problem.

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Kenneth S.

05/03/16