Math 180: Fundamental Theorem of Calculus
1. Let g ( x) 
x

f (t ) dt , where f is the function whose graph is shown below.
0
a. Evaluate g (5) 

5
f (t ) dt
0
b. On what interval(s) of x is g(x) increasing?
c. For what value of x does g(x) have an absolute
minimum value?
d. For what value(s) of x does g(x) = 0?
2. Let g(x) 

x
0
f (t) dt . where f is the function whose graph is below.

Determine if the following statements are TRUE or FALSE.
EXPLAIN (in words) all of your answers!!!
a. g(0)  0

b. g (1)  0
c. g(2)  0


d. g(1)  0
e. g is always increasing for x  0
f. g has a local maximum
at x = 1

f (x)