fix) is continuous on (-ae, ao) and has critical numbers at x a b, c. and d. Use

Question

fix) is continuous on (-ae, ao) and has critical numbers at x a b, c. and d. Use the sign chart f t has a local maximum, a local minimum, or neither at each critical numbes a? Choose the Does fix) have a local minimum a local maximum, or no local extremum at x O A. a local minimum O B no local extremum OC a local maximum Does fix) have a local minimum, a local maximum or no local extremum at x b ? Choose the comect answer below OA, a local maximum B. a local minimum no local extremum C. Does fx) have a local minimum a local maximum a local maximum or no local extremum at xc? Choose the correct answer below extremum at A B. no local extremun a local maximum a loc al minimum

Explanation / Answer

Since on both sides of x=a small sign of f'(x) is + there is no local extremum at x= a. B

At x=b sign of f'(x) changes from + to zero and then from zero to -. Thus it has local maximum at x=b. A

At x=c sign changes from - to zero then to +. Thus it has local minimum at x=c. C

At x=d the function has local maximum. B

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