A chemical reaction releases heat at a differentiable rate (in joules per minute) for

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A chemical reaction releases heat at a differentiable rate

f(t)

(in joules per minute) for

0\le t\le 10

. The total heat released by time

t

minutes is

H(t)=\int_{0}^{t} f(s)\,ds.

After 10 minutes,

H(10)=2400.

Which statement must be true? (a)

f(10)=240\text{ J/min}.

(b) There exists

c

(0,10)

such that

f(c)=240\text{ J/min}

. (c) There exists

c

(0,10)

such that

H'(c)=2400.

(d)

H(5)=1200.