Area Under f'(x) Gives the Change in f(x)

追加: 2026-05-05

[00:00:00]For this question, we have a graph of F prime. We know F of 0 is 5, but we want to find what is F of 1. So, for this one, we could use the fundamental theorem of calculus. And we have the integral from 0 to 1 of F prime of X is equal to F of 1 minus F of 0. So, if we want to find what is F of 1, F of 1 is equal to F of 0 plus the integral from 0 to 1 of F prime of X DX. And now, since we have a graph of F prime, we could just find the area under the curve since we have a straight line segment here.

[00:00:27]So, we're just going to find the area of this triangle and we're going across 1 and up 6. So, we have 1/2 of 1 * 6, which gives us 3. So, now we just plug in F of 0 is equal to 5 plus the area of that triangle is 3. So, our answer is going to be 8, choice D.