Chapter 5, Problem 70RE

a.

To determine

To sketch: The graph of the function $f\left(t\right)=t^2-5t+4$ on the interval $\left[0,6\right]$.

b.

To determine

To compute: The area function $A\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}f\left(t\right)dt}$ and graph the same on the interval $\left[0,6\right]$.

c.

To determine

To show: The local extrema of A occur at the zeroes of f.

d.

To determine

To give: The geometrical and analytical explanation for the observation in part (c).

e.

To determine

To find: The approximate zeroes $x_1,x_2$ of A, other than zero, where $x_1<x_2$.

f.

To determine

To find: The value of b.

g.

To determine

To explain: Whether the statement “if f is an integrable function and $A\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}f\left(t\right)dt}$, is it always true that the local extrema of A occur at the zeroes of f” is true or false.