Question

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

Answer 1

We have a maxima at `x=0`

Explanation:

As `f(x)=-2x^2+9`, `f'(x)=-4x`

As `f'(x)=0` for `x=0`, hence we have a local extrema at `x=-9/4`

Further, `f''(x)=-4` and hence at `x=0`,

we have a maxima at `x=0`

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