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

Question

3085 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-25T18:09:30

I got #23#.

If you think about it, since #x^2# has a minimum, #-x^2 + bx + c# has a maximum (that doesn't require closed bounds).

We should know that:

So, just take the derivative, set it equal to #0#, find the value of #x# (which corresponds to the maximum), and use #x# to find #f(x)#.

#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 #23#.

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

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