Question

If $f$ is a real valued function defined by $f\left(x\right)=x^3+4x+3$, then find $f^{\prime }\left(1\right)$ and $f^{\prime }\left(3\right)$

Answer 1

$f\left(x\right)=x^3+4x+3$

$f^{\prime }\left(x\right)=3x^2+4$

$f^{\prime }\left(1\right)=3(1{)}^2+4$

$=7.$

$f^{\prime }\left(3\right)=3(3{)}^2+4$

$=3\times 9+4$

$=27+4$

$=31$