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

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Answer 1 · 2016-03-19T17:35:23

We have a maxima at $x = 0$ $x=0$

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

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]}

What are the local extrema of f(x)= -2x^2 + 9xf(x)=−2x2+9xf(x)= -2x^2 + 9x?