Question

Why is the answer for letter b 9?

Answer 1

Explanation:

From x=0 to x=1, the function is above the x-axis, so the area is positive.

From x=1 to x=5, the area above the x-axis is greater than the area below the x-axis, so the net area is positive.

From x=5 to x=9, the area above the x-axis is greater than the area below the x-axis, so the net area is positive.

Since the area increases in each interval, the area is a maximum at x=9.

Answer 2

Take a look at the 'proof' below

Explanation:

The graph of the function g(x) is similar to that of the function f(t). The local minimum, local maximum, absolute minimum, maximum etc... of 'x' is always the closest x-intercept of the graph of f(t).

Let's check if this statement is right. The two local minimum(s) of the function f(t) occurs at x = 2, and x = 6. The two local maximum(s) occur at 1/4 and 4. As you can see the maximum / minimum of the function g(x) is always an x-intercept, x = 3, x = 7.

For part (b) the absolute maximum value of the function f(t), is 8. The closest x-intercept is 9, which is our solution.