Megan M.

# Derivatives & the Shapes of Graphs

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

Would someone be able to explain this to me?

Kenneth S.

Doesn't your textbook describe (carefully) the implications of f' = 0 (critical points), intervals of increasing/decreasing, and the implications of f" also??
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05/03/16

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