The fuel economy (in miles per gallon) of a certain car is

Question

E(x) = −0.01x² + 0.54x +10.4, where x is the driving speed (in miles per hour, 20 ≤ x ≤ 60).
At what speed is fuel economy greatest?

Answer 1

Take the first derivative of E(x) wrt x (dE(x)/dx), set it to zero, and solve for x.

 

E(x) = −0.01x² + 0.54x +10.4

 

dE(x)/dx = -0.02x + 0.54

 

0 = -0.02x + 0.54

 

Solve for x