Question

Which of the following is the absolute maximum and minimum of the function: F(x) =2x^2 - 7x -10 on [-1, 3] respectively?

Answer 1

Compute f'(x)

Answer 2

this is the answer

-1, -16 1/8

Answer 3

Quadratic function... anyway, did you compute f'(x)?

Answer 4

yes

Answer 5

y' = 4x -7

Answer 6

And when is this equal to zero?

Answer 7

equate to zero?

Answer 8

Yes

Answer 9

So that means x = 7/4, yes?

Answer 10

yes

Answer 11

Does this fall within your interval?

Answer 12

yes
-1 and 3

Answer 13

So make a note of that. Note that it's a minimum... why?

Answer 14

coz it's positive

Answer 15

What's positive? LOL
Because its second derivative is positive at all points :P
The second derivative is 4, right?

Answer 16

Okay, so that point (x = 7/4) is POSSIBLY an absolute minimum.
What's \[\Large f\left(\frac74\right)=\color{red}?\]

Answer 17

replace all x with 7/4

Answer 18

(Which, with a little brain-crunching, isn't really necessary)
We know that in a quadratic function, the absolute minimum IS at the point where the derivative is zero, namely, at the vertex.

Now check for its absolute maximum.

Just check its value at the endpoints, -1 and 3.

Answer 19

Are you still here?

Answer 20

sorry bro.. My internet went wild