
graph of derivative
The graph of a derivative f '(x) is shown in Figure 5.61. Fill in the table of values for f(x) given that f(0) = 5.
xhttp://www.webassign.net/images/blank.gif0http://www.webassign.net/images/blank.gif123456f(x)5
can someone get me started please...it would really help..thanks....

we can see from the given graph that:
f '(x) = x_____0 <= x <= 1
______1 _____1 <= x <= 3
______x4_____3 <= x <= 5
_______1______5 <= x <= 6
let's integrate f '(x) in the first interval:
f(x) = integ(x dx) = x^2 / 2 + C for all 0 <= x <= 1
now we know that f(0) = 5, thus C = 5
> f(x) = 5  0.5*x^2 0<= x <= 1
which means that f(1) = 4.5
now we proceed to integrate f '(x) in the following interval using the initial condition you've got from the previous interval namely f(1) = 4.5, we continue this way till the last interval...