Exercise To Try 8 For the curve f (x) = 2r-9a2 + 12r - 5, find (i) the local marimum and minimum values, (ii), the intervals on which f is increasing or decreasing, and (ii) the intervals of concavity and the inflection points. (a) Find critical points: (find where f'(r) = 0 or where f'(x) is undefined). (b) Use 2nd derivative test to determine which of the critical points are local min/max. (c) Use the 1st derivative test for any inconclusive points, and to find where f(r) is in- creasing/decreasing.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Exercise To Try 8 For the curve f (x) = 2r – 9a2 + 12r – 5, find (i) the local marimum
and minimum values, (ii), the intervals on which f is increasing or decreasing, and (iii) the
intervals of concavity and the inflection points.
(a) Find critical points: (find where f'(a) = 0 or where f'(7) is undefined).
(b) Use 2nd derivative test to determine which of the critical points are local min/max.
(c) Use the 1st derivative test for any inconclusive points, and to find where f(x) is in-
creasing/decreasing.
(d) Use f(z)" to determine where the function is concave up (CU) or concave down (CD),
and find any inflection points.
Can you draw a rough sketch
of the curve?
Transcribed Image Text:Exercise To Try 8 For the curve f (x) = 2r – 9a2 + 12r – 5, find (i) the local marimum and minimum values, (ii), the intervals on which f is increasing or decreasing, and (iii) the intervals of concavity and the inflection points. (a) Find critical points: (find where f'(a) = 0 or where f'(7) is undefined). (b) Use 2nd derivative test to determine which of the critical points are local min/max. (c) Use the 1st derivative test for any inconclusive points, and to find where f(x) is in- creasing/decreasing. (d) Use f(z)" to determine where the function is concave up (CU) or concave down (CD), and find any inflection points. Can you draw a rough sketch of the curve?
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