Chapter 2.2, Problem 112E

To determine

To find: The height of the tree when it is diminishing returns.

Answer to Problem 112E

G is diminishing can be given as by put $t=15.22$ .

  $G=27.3$.

Explanation of Solution

Given information: As $G=-0.003t^3+0.137t^2+0.0458t-0.839$

When G is the height of the tree and t is the age in years

As $G=-0.003t^3+0.137t^2+0.0458t-0.839$

For diminishing returns

  $\begin{array}{l}{G}^{\prime }=-0.003\times 3t^2+0.137\times 2t+0.0458\\ {G^{\prime }}^{\prime }=-0.003\times 6t+0.137\times 2\end{array}$

Now, $G^{″}=0$

  $\begin{array}{l}\therefore 0.003\times 6t=0.137\times 2\\ \therefore t=\frac{0.137\times 2}{0.003\times 6}=15.22\text{ years}\end{array}$

G is diminishing returns at $t=15.22$ years and G is diminishing can be given as by put $t=15.22$ .

  $\begin{array}{l}$ G=-0.003({15.22}^{)3}+0.137{(15.22)}^2+0.0458(15.22)-0.839$G=27.3\end{array}$