# What is the maximum value that the graph of #f(x)= -x^2+8x+7#?

##### 1 Answer

Jul 25, 2016

I got

If you think about it, since

We should know that:

- The slope is
#0# when the slope changes sign. - The slope changes sign when the graph changes direction.
- One way a graph changes direction is at a maximum (or minimum).
- Therefore, the derivative is
#0# at a maximum (or minimum).

So, just take the derivative, set it equal to

#f'(x) = -2x + 8# (power rule)

#0 = -2x + 8#

#2x = 8#

#color(blue)(x = 4)#

Therefore:

#f(4) = -(4)^2 + 8(4) + 7#

#= -16 + 32 + 7#

#=> color(blue)(y = 23)#

So your maximum value is

#y = -x^2 + 8x + 7# :

graph{-x^2 + 8x + 7 [-7.88, 12.12, 16.52, 26.52]}