Chapter 11.6, Problem 59E

Grades⁶² A productivity formula for a student’s performance on difficult English examination is

$g=4tx-0.2t^2-10x^2\left(t<30\right),$

where g is the score the student can expect to obtain, t is the number of hours of study for the examination, and x is the student’s grade-point average.

a. For how long should a student with a 3.0 grade-point average study to score 80 on the examination?

b. Find $\frac{dt}{dx}$ fora student who earns a score of 80, evaluate it when $x=3.0,$ andinterpret the result.