Exercise Four: Solution (Calculus)

Problem:
Find the non-negative value of x for which T is a maximum. What is the corresponding maximum value?

Solution:
Take the derivative of T with respect to x.

Set the derivative equal to zero and solve for x.


Since x must not be negative, disregard the solution x = –1.
Note that

for(T is increasing to the left of 1)

and

for(T is decreasing to the right of 1)

Thus x = 1 corresponds to a maximum.
Find T.

Answer:
T has a maximum value of 0.07 when x is 1.

What happens to the function T when x takes the value -1?

Exercise Three Exercise Five