# How do you find the maximum value of #y = -2x^2 + 36x - 177#?

##### 1 Answer

I got

Since this function is a **quadratic** (**negative**, this function has one maximum (look at the shape of any

If you take the **first derivative**, *instantaneous slope* at a maximum or minimum, and you now know that it will be a maximum.

#d/(dx)[-2x^2 + 36x - 177]#

#= -4x + 36#

(refer back to the Power Rule:#d/(dx)[x^n] = nx^(n-1)# .)

So, setting it equal to

#0 = -4x + 36#

#4x = 36#

#color(green)(x = 9)#

Now that you know what

#color(blue)(f(9)) = -2(9)^2 + 36(9) - 177#

#= -162 + 324 - 177#

#= -339 + 324#

#= color(blue)(-15)#

So, your maximum value is