Let f(x)=−1−x^2. Find each of the following: (f(6)-f(3))/6-3, (f(3+h)-f(3))/h, lim h→0 (f(3+h)-f(3))/h

Answer 1

f(x) = -1-x^2

f(6) = -1-36 = -37

f(3) = -1-9 = -10

[f(6)-f(3)]/(6-3)= -37--10)/3 = -27/3 = -9

f'(x)= -2x

f'(3) = -2(3) = -6 = [f(3+h)-f(3)]/h as h approaches zero