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Does anyone know the answer (s) to this?

Jimmy Perdon

New member
May 3, 2021
A simplified model of the power P required to sustain the motion of an electric car at speed v experiencing nonzero drag can be modeled by the equation:

P = Av^2 + (B/v)
(where A and B are positive constants.)

(a) What speed vP minimizes power?
(b) What power does the speed in (a) require?
(c) Suppose that an electric car has a usable store E of energy. How far dP can the electric car travel at the
speed found in (b)?


Staff member
Feb 5, 2013
Here's the derivative for the function of power, \(\displaystyle P=Av^2+\frac{B}{v} (\text{Where }A\text{ and }B\text{ are positive constants)} \) that they give in the introduction to the problem:

\(\displaystyle P'(v)=2Av-\frac{B}{v^2} \)

To answer \(\displaystyle \text{(a) What speed }vP\text{ minimizes power?} \) we set this expression equal to \(\displaystyle 0 \) and solve for \(\displaystyle v \):

2Av-\frac{B}{v^2}&=0 \\
2Av&=\frac{B}{v^2} \\
2Av\cdot\frac{v^2}{B}&=\frac{B}{v^2}\cdot\frac{v^2}{B} \\
\frac{2Av\cdot v^2}{B}&=1 \\
\frac{2Av^3}{B}\cdot\frac{B}{2A}&=1\cdot\frac{B}{2A} \\
v^3&=\frac{B}{2A} \\
v=\sqrt[3]{\frac{B}{2A}} \\

Now we need to determine if this result is a minimum or a maximum and we do this by examining the concavity of the graph of \(\displaystyle P \)

I'll let you take a look at the graph and experiment with the different values for \(\displaystyle A \) and \(\displaystyle B \). As a suggestion, take a look at the graph when \(\displaystyle A \) and \(\displaystyle B \) are different signs.
Last edited:


Well-known member
MHB Math Helper
Mar 1, 2012