Question

Can anyone just explain the steps to this problem I keep messing up and I need some guidance. Thank you!

Answer 1

Answer:

(B) 1

Step-by-step explanation:

g(x) = ∫₂ˣ f(t) dt

Use second fundamental theorem of calculus to find g'(x).

g'(x) = f(x) d(x)/dx − f(2) d(2)/dx

g'(x) = f(x)

g(x) is a maximum when g'(x) = 0.

0 = f(x)

x = 3

So the maximum value of g(x) is:

g(3) = ∫₂³ f(t) dt

g(3) = ½ (2) (1)

g(3) = 1