Real function/Extrema/4x^3+3x^2-x+2/Tangent from -3 to 3/Exercise

Consider the function

$f\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto f(x)=4x^{3}+3x^{2}-x+2.$

Find the point ${}a\in [-3,3]$ such that the tangent of the function at ${}a$ is parallel to the secant between ${}-3$ and ${}3$.

Create a solution