Find the critical numbers of f and classify the extreme values given x ∈ [0, 10] and f(x) = x^2 -16x +2

I know to find critical points;
f'(x) = 2x-16 = 0; x=8

So the critical points would be 0, 8, 10 because I have to include the endpoints? However the answer choices are not matching up...

a) Critical nos. 0, 8; local and absolute min f(8) = -62; absolute max f(10) = -58.
b) No critical numbers, no extreme values.
c) Critical no. 0; local max f(0) = 2.
d) Critical no. 8, 10; local max f(10) = f(8) = -58.
e) Critical no. 8; absolute max f(0) = 2; local and absolute min f(8) = -62.

Question

Find the critical numbers of f and classify the extreme values given x ∈ [0, 10] and f(x) = x^2 -16x +2

I know to find critical points;
f'(x) = 2x-16 = 0; x=8

So the critical points would be 0, 8, 10 because I have to include the endpoints? However the answer choices are not matching up...

a) Critical nos. 0, 8; local and absolute min f(8) = -62; absolute max f(10) = -58.
b) No critical numbers, no extreme values.
c) Critical no. 0; local max f(0) = 2.
d) Critical no. 8, 10; local max f(10) = f(8) = -58.
e) Critical no. 8; absolute max f(0) = 2; local and absolute min f(8) = -62.

anonymous · Answer

Right now I'm going with e. since maybe you dont include the endpoints and the absolute max and min are correct. But I would like someone to confirm please D: