for the function ( f(x)=3x^{3}-2x^{2}+13x + 8 ), find ( f^{primeprime}(x) ). then find ( f^{primeprime}(0) )…

for the function ( f(x)=3x^{3}-2x^{2}+13x + 8 ), find ( f^{primeprime}(x) ). then find ( f^{primeprime}(0) ) and ( f^{primeprime}(9) ).\n( f^{primeprime}(x)=)\nselect the correct choice below and fill in any answer boxes in your choice.\na. ( f^{primeprime}(0)=) (simplify your answer.)\nb. ( f^{primeprime}(0) ) is undefined.\nselect the correct choice below and fill in any answer boxes in your choice.\na. ( f^{primeprime}(9)=) (simplify your answer.)\nb. ( f^{primeprime}(9) ) is undefined.

for the function ( f(x)=3x^{3}-2x^{2}+13x + 8 ), find ( f^{primeprime}(x) ). then find ( f^{primeprime}(0) ) and ( f^{primeprime}(9) ).\n( f^{primeprime}(x)=)\nselect the correct choice below and fill in any answer boxes in your choice.\na. ( f^{primeprime}(0)=) (simplify your answer.)\nb. ( f^{primeprime}(0) ) is undefined.\nselect the correct choice below and fill in any answer boxes in your choice.\na. ( f^{primeprime}(9)=) (simplify your answer.)\nb. ( f^{primeprime}(9) ) is undefined.

Answer

Explanation:

Step1: Differentiate (f(x)) once

Use the power rule ((x^n)^\prime = nx^{n - 1}). For (f(x)=3x^{3}-2x^{2}+13x + 8), (f^\prime(x)=3\times3x^{2}-2\times2x+13\times1+0=9x^{2}-4x + 13).

Step2: Differentiate (f^\prime(x)) to get (f^{\prime\prime}(x))

Differentiate (f^\prime(x)=9x^{2}-4x + 13) again. (f^{\prime\prime}(x)=9\times2x-4\times1+0 = 18x-4).

Step3: Find (f^{\prime\prime}(0))

Substitute (x = 0) into (f^{\prime\prime}(x)). (f^{\prime\prime}(0)=18\times0-4=-4).

Step4: Find (f^{\prime\prime}(9))

Substitute (x = 9) into (f^{\prime\prime}(x)). (f^{\prime\prime}(9)=18\times9-4=162 - 4=158).

Answer:

(f^{\prime\prime}(x)=18x - 4); (A. f^{\prime\prime}(0)=-4); (A. f^{\prime\prime}(9)=158)