question on a given interval a,b, a polar function r = f(θ) goes from increasing to decreasing 9 times and…

question on a given interval a,b, a polar function r = f(θ) goes from increasing to decreasing 9 times and decreasing to increasing 3 times. using this information, make an inference about the total number of relative maxima, relative minima, and relative extrema the function has on the interval a,b. if you cannot make an inference, write 0. answer relative maxima relative minima relative extrema

question on a given interval a,b, a polar function r = f(θ) goes from increasing to decreasing 9 times and decreasing to increasing 3 times. using this information, make an inference about the total number of relative maxima, relative minima, and relative extrema the function has on the interval a,b. if you cannot make an inference, write 0. answer relative maxima relative minima relative extrema

Answer

Explanation:

Step1: Define relative maxima and minima

A function changes from increasing to decreasing at a relative maximum and from decreasing to increasing at a relative minimum.

Step2: Determine number of relative maxima

Since the function goes from increasing to decreasing 9 times, the number of relative maxima is 9.

Step3: Determine number of relative minima

Since the function goes from decreasing to increasing 3 times, the number of relative minima is 3.

Step4: Calculate number of relative extrema

Relative extrema are the set of relative maxima and minima. So, the number of relative extrema is (9 + 3=12).

Answer:

9 3 12