Textbook Problem

Grades²⁰ A production formula for a student’s performance on a difficult English examination is given by

$g\left(t,x\right)=4tx-0.2t^2-x^2$, where g is the grade the student can expect to get, t is the number of hours of study for the examination, and x is the student’s grade-point average.

a. Calculate $g_t\left(10,3\right)$ and $g_x\left(10,3\right)$, and interpret the results.

b. What does the ratio $\frac{g_t\left(10,3\right)}{g_x\left(10,3\right)}$ tell about the relative merits of study and grade-point average?