Chapter 5, Problem 112RE

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 $A\left(x\right)$ and draw its graph.

c.

To determine

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

d.

To determine

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

e.

To determine

To find: The approximate zeros of $A$, other than 0, and call them $x_1$ and $x_2$, where $x_1<x_2$.

f.

To determine

To find: The value of $b$ such that the area bounded by the graph of $f$ and the $t$-axis on the interval $\left[0,x_1\right]$ equal to the area bounded by the graph of $f$ and the $t$-axis on the interval $\left[x_1,b\right]$.

g.

To determine

Whether the local extrema of A occurs are zeros of f or not.