A continuous function g is defined on the closed interval [0,5].
An accumulation function is defined by
F(x)=∫x5g(t)dt,0≤x≤5.
Answer the following questions about F.
(a) Determine F′(x) in terms of g. Clearly indicate any factors or signs that arise from the structure of the integral.
(b) Explain, without performing any numerical computation, why F′(x) has the sign you found in part (a). Relate your explanation to the direction in which the integral accumulates area.
(c) Suppose g(t)>0 for all t in (0,5). Describe the monotonicity of F on (0,5) and justify your conclusion using your result from part (a).