Find the absolute maximum and minimum values of the function over the indicated​ interval, and indicate the​ x-values at which they occur.

Question

Find the absolute maximum and minimum values of the function over the indicated​ interval, and indicate the​ x-values at which they occur.

f(x)=2x+9

​(A) ​[0​,8​]    ​ (B) [−2,5]

​

(A) Find the first derivative of f.

f′(x)= ___________

​(Simplify your​ answer.)

Answer 1

for [0,8] max is 25, 9 is min 2(8)+9 = 16+9=25, 2(0)+9 = 9

f(0)=9, f(8)=25

for [-2,5] max is 19, min 5 2(5)+9 = 19, 2(-2)+9 = 5

f(5)=19, f(-2)=5

derivative is 2, just the coefficient of the x term

f'(x) = 2