Find the open intervals on which the function is increasing and decreasing. b. I

Question

Find the open intervals on which the function is increasing and decreasing. b. Identity the function's local and absolute extreme values, if any, saying where they occur. f(r) = 2r^3 +17r a. Find the open intervals on which the function is increasing and decreasing. A. The function f is increasing on the interval (-infinity, 0) and decreasing on (0, theta). B. The function f is decreasing on the interval (- infinity, infinity). C. The function f is increasing on the interval (- infinity, infinity). D. The function f is decreasing on the interval (- infinity, 0) and increasing on (0, infinity). b. Identify the function's local extreme values, if any. A. The function f has no local extrema. B. The function f has a local minimum at r = 0. C. The function f has a local maximum at r = 0. Identify the function's absolute extreme values if any A. the function f has an absolute maximum at r = 0 B. The function f has a local maximum at r = 0, but not an absolute maximum. C. The function f has no absolute extrema. D. The function f has an absolute minimum at r = 0

Explanation / Answer

a) the function given is 2r^3 +17r

f'(r) =6r^2+17

6r^2 +17 =0

No real solution for r.

f''(r) =12r

The function has no extreme points and is increasing for all r.

so option c is correct.

b)option A is correct as function has no extreme values

c)option C is correct the function has no absolute extreme values.

Thank you

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