How do you find the max or minimum of #f(x)=-5x^2+8x#?

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Answer 1 · 2017-12-18T16:22:24

#=> (4/5 , 16/5 ) # is our maximum

For the question its a good idea to sketch the function:

We can factor #f(x)#:

#f(x) = x(-5x+8)#

Now fidnig the roots:

#x(-5x+8) = 0#

#=> x = 0 , x = 8/5 #

These are our roots:

As its a negative coefficiant for #x^2# its a negative porabola:

graph{-5x^2+8x [-4.473, 6.48, -1.27, 4.207]}

The #x# point for the vertex, is half way between the roots:

#x = 4/5 #

Plugging #x= 4/5# into the equation:

#y = 16/5 #

From the image this is a max

#=> (4/5 , 16/5 ) # is our maximum