# What are the local extrema of f(x)= -2x^2 + 9x?

Mar 19, 2016

We have a maxima at $x = 0$

#### Explanation:

As $f \left(x\right) = - 2 {x}^{2} + 9$, $f ' \left(x\right) = - 4 x$

As $f ' \left(x\right) = 0$ for $x = 0$, hence we have a local extrema at $x = - \frac{9}{4}$

Further, $f ' ' \left(x\right) = - 4$ and hence at $x = 0$,

we have a maxima at $x = 0$

graph{-2x^2+9 [-5, 5, -10, 10]}