Chapter 4.7, Problem 31E

(a)

To determine

Tofind at what distance hummingbird does feed.

Answer to Problem 31E

  $4$ Meters.

Explanation of Solution

Given:

A portion of the path that a hummingbird flies while feeding can be modeled by the function

$f(x)=-\frac{1}{5}x{(x-4)}^2(x-7),0\le x\le 7$

Calculation:

The hummingbird feeds each time it is at ground level.

Therefore the distance is-

$\begin{array}{}$ f(x)=-\frac{1}{5}x{(x-4)}^2(x-7)$$ 0=-\frac{1}{5}x{(x-4)}^2(x-7)$$ 0=x{(x-4)}^2(x-7)$$ x=0,x=4,x=7$\end{array}$

The humming bird feed at the distance of $4$ meters.

(b)

To determine

To write a function to model the path of the Second hummingbird.

Answer to Problem 31E

$f(x)=-\frac{1}{5}x{(x-6)}^2(x-7)$ .

Explanation of Solution

Given:

A second hummingbird feeds 2 meters farther away than the first hummingbird and flies twice as high.

Calculation:

The following will be the model function for the second bird

$f(x)=-\frac{1}{5}x{(x-6)}^2(x-7)$

The humming bird feed at the distance of $4+2=6$ meters.