S(x)=-x^2+20x+80

Question

he registrar's office at a local community college has found that the average number of students attending intermediate algebra classes is approximated by S(x)=-x^2+20x+80, where x is the number of hours that the College Learning Center is open daily. Find the number of hours that the center should be open so that the number of students attending class is a maximum. What is this maximum number of students

Answer 1

y=num lerners=80+20x-x^2

wanna get max...so get dy/dx...slope & set tu zero

dy/dx=20-2x=0 at x=10

at x=10, y=80+300-100=280