A differentiable function g is defined on the real numbers. Selected values of g and g′ are shown in the table below.
x
0
1
2
3
4
5
g(x)
2
1
−1
−2
−3
−4
a) Let F be the antiderivative of g satisfying F(0)=7. Explain why F is strictly decreasing on the interval 2≤x≤5.
b) Without evaluating any definite integrals, determine which is larger, F(3) or F(5). Provide a justification based on the given information about g.
(a) Explain why F is strictly decreasing on the interval 2≤x≤5.
(b) Without evaluating any definite integrals, determine which value is larger, F(3) or F(5), and justify your conclusion.