Question

Problem 49.
Find the critical values

f(x) = (4x^2 - 9) / x

Answer 1

before differentiating, I would simplify it to
f(x) = 4x - 9/x

then f'(x) = 4 + 9/(x^2)

set that equal to zero, and solve to find any maximum and minimum values

f"(x) = -18/(x^3)

when you set the second derivative equal to zero, there is no solution, so there is no point of inflection.

Use your second derivative to determine if the curve is concave up or down.
If f" is positive, the graph is concave up
etc. you should know these properties to do these kind of questions.

Answer 2

Thanks.