Chapter 1.8, Problem 4CYU

To determine

To compare: The highest point of fuel efficiency of two cars A and B.

Answer to Problem 4CYU

The highest point of efficiency for car $A$ is $53mpg$ while that for car $B$ is near about $58mpg$ .

Explanation of Solution

Given information: Description about fuel efficiency car $A$ and graph concerning car $B$ .

Calculation:

Car $A$ reaches relative maximum efficiency $53mpg$ at a speed of $25mph$ . While at $25mph$ car $B$ ’s efficiency is about $40mpg$ . At $41mph$ car $A$ ’s efficiency gets down to $37mpg$ while at this point car $B$ ’s efficiency is about $47mpg$ . The highest point of efficiency for car $A$ is $53mpg$ while that for car $B$ is near about $58mpg$ . For car $A$ the certain recession starts after $60mph$ while for car $B$ efficiency is still increasing after $60mph$ , recession starts after $63mph$ .

For car $A$ :

Increasing: $0<x<25$ and $41<x<60$

Decreasing: $25<x<41$ and $60<x<120$

Relative Maximum: $53mpg$

Relative Minimum: $17mpg$

For car $B$ :

Increasing: $0<x<15$ and $23<x<32$ and $57<x<63$

Decreasing: $15<x<23$ and

  $32<x<57$ and $63<x<120$

Relative Maximum: $58mpg$

Relative Minimum: $23mpg$