Question

for f(x)=-x^2 +1, which value is the largest magnitude?
a) average rate of change from x=-1 to x=1
b) instanteneuous rate of change at x=3
c) instanteneous rate of change at x=0
average rate of change from x=-4 to x=0

Answer 1

a) (f(1)-f(-1))/(1 - (-1)) = 0
b) f'(x) = -2x. f'(3) = -6
c) f'(0) = 0
d) (f(0)-f(-4))/(0-(-4)) = 4

pick the greatest magnitude.