What are the extreme values of 2x2-8x plus 9?

Answer 1

Given:

f(x) = 2x2 - 8x + 9

This function describes a parabola, which only has one extreme value. To find that value, you can take the derivative of the function, and use that to find the point at which it has a slope of zero:

f'(x) = 4x - 8

if f'(x) = 0, then:

0 = 4x - 8

∴4x = 8

∴ x = 2

Now we work out the corresponding value for f(2):

f(2) = 2(2)2 - 8(2) + 9

= 8 - 16 + 9

= 1

So the extreme value for this function is 1, which occurs at the point (2, 1)