Question

What is the minimum value of the function over the interval -5 < x < 5?

h(x) = log[(x – 3)^2 + 2]

Answer 1

Answer: ln(2)

Explanation:

In order to minimize ln[(x – 3)^2 + 2], we have to minimize [(x – 3)^2 + 2] since natural log is an increasing function

For that, it suffices to minimize (x – 3)^2, which is non-negative for all real numbers x

As such, the minimum value is achieved when x - 3 = 0; - 5 < 3 < 5

Substitute x = 3 in the original equation to get ln(2)