Barrons AP Calculus

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(a)

Example 43 __

The function f(t) is graphed in Figure N6–22a. Let

Figure  N6–22a

What    is  the domain  of  F?

Find    x,  if  F   ′(x)    =   0.

Find    x,  if  F(x)    =   0.

Find    x,  if  F(x)    =   1.

Find    F   ′(6).

Find    F(6).

Sketch  the complete    graph   of  F.

SOLUTIONS:

The domain  of  f   is  [−2,1]  and [2,6].  We  choose  the portion of  this    domain

that    contains    the lower   limit   of  integration,    4.  Thus    the domain  of

.