Question

Find the maximum or minimum of the following quadratic function: y = -10x^2 + x - 10.
A. -40
B. -10
C. 10
D. -399/40

Answer 1

Maximum = -399/40

Answer 2

y=f(x). Take dy/dx ( f'(x) ) to get -20x+1. Critical points are where f'(x)=0. Solving:

0=-20x+1
20x=1
x=1/20
y=f(x)=f(1/20)=-9.975=-399/40

Answer 3

If you are in pre-calculus and have not been taught derivatives yet, put the equation in vertex form to find your min/max.

Answer 4

Looking at f(0) to the left of critical point (=-10) and f(1) to the right (=-19), you can tell that this point is a relative maximum. Because the parabola opens down, this is the 'biggest' the function can get (absolute maximum). You could have seen all of this from graphing the function.

Answer 5

Thanks Guys.