A patient's pulse is measured three times. The results are 70 bmp, 80 bpm,and 120bpm. The doctor would like to find a number which most accurately represents the patient's pulse. To do so, they minimize:

p(x)=(x70)²+(x80)²+(x120)²

a) Find all the critical points ofp(x).

b) Calculate which values ofxminimizesp(x).

c) Briefly explain why the doctor might choose this functionp(x)to minimize.