Question

Which of the ten basic functions in our toolkit have an infinite number of local extrema?

a) cos(x)
b) sin(x), cos(x)
c) In(x), cos(x)
d) sin(x), x2

Answer 1

The functions sin(x) and cos(x) have an infinite number of local extrema.

Step-by-step explanation:

In mathematics, the term 'extrema' refers to the maximum and minimum values of a function.

The local extrema occur at points where the function reaches a high or low point within a specific interval.

To determine if a function has an infinite number of local extrema, we need to analyze its periodicity.

The function cos(x) has an infinite number of local extrema because it is periodic and repeats its values over an infinite range.

Similarly, the function sin(x) and cos(x) also have an infinite number of local extrema.

Therefore, the correct answer is option b) sin(x), cos(x).