for the function f(x)=5x³ - 3x² + 2x + 3, find f(x). then find f(0) and f(8).\nf(x)= \nselect the correct…

for the function f(x)=5x³ - 3x² + 2x + 3, find f(x). then find f(0) and f(8).\nf(x)= \nselect the correct choice below and fill in any answer boxes in your choice.\na. f(0)= (simplify your answer.)\nb. f(0) is undefined.\nselect the correct choice below and fill in any answer boxes in your choice.\na. f(8)= (simplify your answer.)\nb. f(8) is undefined.

for the function f(x)=5x³ - 3x² + 2x + 3, find f(x). then find f(0) and f(8).\nf(x)= \nselect the correct choice below and fill in any answer boxes in your choice.\na. f(0)= (simplify your answer.)\nb. f(0) is undefined.\nselect the correct choice below and fill in any answer boxes in your choice.\na. f(8)= (simplify your answer.)\nb. f(8) is undefined.

Answer

Explanation:

Step1: Differentiate the function ( f(x) = 5x^{3}-3x^{2}+2x + 3 )

Using the power rule ( \frac{d}{dx}(x^{n})=nx^{n - 1} ), we have: ( f^{\prime}(x)=\frac{d}{dx}(5x^{3})-\frac{d}{dx}(3x^{2})+\frac{d}{dx}(2x)+\frac{d}{dx}(3) ) ( f^{\prime}(x)=5\times3x^{2}-3\times2x + 2\times1+0 ) ( f^{\prime}(x)=15x^{2}-6x + 2 )

Step2: Find ( f^{\prime}(0) )

Substitute ( x = 0 ) into ( f^{\prime}(x) ): ( f^{\prime}(0)=15\times0^{2}-6\times0 + 2 ) ( f^{\prime}(0)=2 )

Step3: Find ( f^{\prime}(8) )

Substitute ( x = 8 ) into ( f^{\prime}(x) ): ( f^{\prime}(8)=15\times8^{2}-6\times8 + 2 ) ( f^{\prime}(8)=15\times64-48 + 2 ) ( f^{\prime}(8)=960-48 + 2 ) ( f^{\prime}(8)=914 )

Answer:

( f^{\prime}(x)=15x^{2}-6x + 2 ); ( A. f^{\prime}(0)=2 ); ( A. f^{\prime}(8)=914 )