Barrons AP Calculus

(i)

(ii)

(iii)

Here is the completed table:

Example 31 __

The graph of the function f(t) is shown in Figure N6–14.

Figure  N6–14

Let . Decide whether each statement is true or false; justify your

answers:

If  4   <   x   <   6,  F(x)    >   0.

If  4   <   x   <   5,  F   ′(x)    >   0.

F′′(6)  >   0.

SOLUTIONS:

(i) is true. We know that, if a function g is positive on (a,b), then ,

whereas if g is negative on (a,b), then . However, the area above the

x-axis between x = 1 and x = 4 is greater than that below the axis between 4 and

6. Since