critical numbers

Question

Find the critical numbers of the function. (Enter your answers as a comma-separated list.)

g(t) = 2t ln t

Answer 1

To find critical numbers, take the derivative. The derivative of 2t ln t is found using the product rule so it is (2t)'(ln(t)) + (2t)(ln(t))' = 2ln(t) + 2t(1/t) = 2ln(t) + 2. Set the derivative equal to zero and solve.

2ln(t) + 2 = 0

2ln(t) = -2

ln(t) = -1

Re-writing this as an exponential you get:

e^-1 = t or t = 1/e

That is the critical number.