Please explain and answer the question

Consider the function f(x) = (x - x2) on the interval [-1, 1]. Sketch the function, and highlight the minima and maxima, and label them as local or absolute. a) Find all the critical points of f(x). b) Identify all the local and absolute maxima and minima. c) Sketch the function, and highlight the minima and maxima, and label them as local or absolute.A patient's pulse is measured three times. The results are 70 bmp, 80 bpm, and 120 bpm.The doctor would like to find a number which most accurately represents the patient's pulse. To do so, they minimize: p(x) = (x 70)2 + (x 80)2 + (x 120)2 a) Find all the critical points of p(x). b) Calculate which values of x minimizes p(x). 0) Briefly explain why the doctor might choose this function p(x) to minimize