Question: The graph of a differentiable function \(f\) on the close interval [1, 7] is shown. Let \(h\left( x \right)=\int\limits_{1}^{x}{f\left( t \right)dt}\), for \(1\le x\le 7\).

(a) Find \(h\left( 1 \right)\)

(b) Find \(h'\left( 4 \right)\)

(c) On what interval is the graph of h concave upward?

(d) Find the value of x at which h has its maximum on the closed interval [1, 7].