Understanding Local Minimums in Functions

The video tutorial explores how to identify a local minimum of a function with a value of 1. It examines three functions, f(x), g(x), and h(x), to determine which one has a local minimum at this value. The analysis shows that f(x) and g(x) do not have a local minimum at 1, while h(x) does, as it decreases into the value and increases out of it.

What is the range of x values given in the problem?

• From -2 to 2

• From -3 to 3

• From -4 to 4

• From -5 to 5

Which functions are identified as candidates for having a local minimum value of 1?

• f(x), g(x), and h(x)

• g(x) and h(x) only

• f(x) and h(x) only

• f(x) and g(x) only

Tags

CCSS.HSF-IF.C.7D

What happens to f(x) as it approaches and leaves the value 1?

• It increases into 1 and continues increasing

• It decreases into 1 and continues decreasing

• It decreases into 1 and increases out of it

• It increases into 1 and decreases out of it

What is the behavior of g(x) at the point where it hits 1?

• It decreases into 1 and continues decreasing

• It increases into 1 and decreases out of it

• It increases into 1 and continues increasing

• It decreases into 1 and increases out of it

What is the behavior of h(x) at the point where it hits 1?

• It increases into 1 and continues increasing

• It decreases into 1 and continues decreasing

• It increases into 1 and decreases out of it

• It decreases into 1 and increases out of it