Optimization problem with graph

[2000xjclassic]

Homework Statement

We are given a graph of gallons of fuel per hour versus miles per hour and asked what speed should be used to maximize fuel efficiency and also what is the optimal speed(are these two the same thing).

Homework Equations

I understand optimization using the first derivative when given an equation, I am having a problem with figuring out what to do with only a graph

The Attempt at a Solution

I have graphed the first derivative. should I use the zero points from the first derivative graph to optimize the fuel efficiency?

Thanks in advance.
Chris

 

[HallsofIvy]

Homework Statement

We are given a graph of gallons of fuel per hour versus miles per hour and asked what speed should be used to maximize fuel efficiency and also what is the optimal speed(are these two the same thing).

"Optimal" simply means "best". IF "optimal" here means "best fuel efficiency", then they are the same.

Homework Equations

I understand optimization using the first derivative when given an equation, I am having a problem with figuring out what to do with only a graph

The Attempt at a Solution

I have graphed the first derivative. should I use the zero points from the first derivative graph to optimize the fuel efficiency?

Thanks in advance.
Chris

Yes, the max or min points will be where the first derivative is 0. I don't know that you really needed to graph the entire derivative. The derivative will be 0 where the original graph has a horizontal tangent.