Question

Find the local maxima or local minima of $f\left(x\right)=x^3-x^2+9x+15$. Also find the local maximum or local minimum values as the case may be.

Answer 1

$f\left(x\right)=x^3-x^2+9x+15$

$\frac{dy}{dx}=3x^2-2x+9\frac{dy}{dx}=03x^2-2x+9=0D=4-4(3\times 9)D<0$

hence $\frac{dy}{dx}>0$ for all values of $x$

$f\left(x\right)$ function is always an increasing funtion

hence $nomaximaorminima$