calculus derivatives

Question

Let 𝑓(𝑥)=2𝑥^2−8𝑥+5.

Find the extreme values of 𝑓 on [0,5].

(Give your answers as whole numbers.)

find the maximum and minimum

Find the extreme values of 𝑓 on [−4,1].

(Give your answers as whole numbers.)

find the maximum and minimum

Answer 1

f(x) = 2x² - 8x + 5

f'(x) = 4x - 8. This means there is one critical point at x = 2. Having said that, we are looking for extreme values on specific bounded intervals.

[0 , 5] first. f(0) = 5 and f(5) = 2(5²) - 8(5) +5 = 15. At x= 2, f(2) = 2 (2²)- 8(2) + 5 = -3

So max is 15 and minimum is 3

On interval [-4, 1] there are no critical points, so f(1) = 2-8+5= -1 and f(-4) = 2 (-4)²-8(-4) +5 = 69

Max is 69 and min is -1