Find the absolute extreme values of the function on the interval.
-$$f ( x ) = 2 x - 3 , - 3 \leq x \leq 4$$
A) absolute maximum is 5 at x = 4; absolute minimum is - 9 at x = -3
B) absolute maximum is 11 at x = -4; absolute minimum is - 9 at x = 3
C) absolute maximum is 11 at x = 4; absolute minimum is - 3 at x = -3
D) absolute maximum is 5 at x = -3; absolute minimum is - 3 at x = 4

Question

Quizplus · Accepted Answer

To find the absolute extreme values of the function, we need to find the critical points and the endpoints of the interval.
Critical point: 
$$f'(x)=2$$
The derivative is a constant, so there is no critical point in the interval.
Endpoints: 
$$f(-3)=2(-3)-3=-9$$
$$f(4)=2(4)-3=5$$
Therefore, the absolute maximum value of the function is 5 at x=4 and the absolute minimum value of the function is -9 at x=-3. The correct choice is A.

Find the Absolute Extreme Values of the Function on the Interval