It is given that $\mathrm{f}(x) = \frac{1}{3}x^3 + 2x^2 - 5x$. $\mathrm{f}(x)$ has a maximu

Question

It is given that $\mathrm{f}(x) = \frac{1}{3}x^3 + 2x^2 - 5x$. $\mathrm{f}(x)$ has a maximum point at $M$, and a point of inflexion at $N$. Find $\mathrm{f}'(x)$. Find the $x$-coordinate of $M$. Find the $x$-coordinate of $N$. The line $L$ is the tangent to the curve of $\mathrm{f}$ at $(3, 12)$. Find the equation of $L$ in the form $y = ax + b$.

Accepted Answer

(a) $\mathrm{f}\,	ext{ }\!\!'\!\!	ext{ }\left( x ight)={{x}^{2}}+4x-5$ (b) $x=-5$ (c) $x=-2$ (d) $y=16x-36$

Differentiation - Tangents and Normals at a Point

Differentiation - Tangents and Normals at a Point