Question

Suppose that f (x) is a function such that the relationship given below is true.
f (3 + h) - f (3) = 9h^2 + 8h

(a) What is f '(3)?


(b) What is the slope of the secant line through (3, f (3)) and (7, f (7))?

Answer 1

Please do not use shortcuts(from future chapters) and show steps so i can see whats going on

Answer 2

if you recall the definition of a derivative is
lim h->0 [f(x+h)-f(x)]/h

(a)
you're given:
f (3 + h) - f (3) = 9h^2 + 8h
just divide h so that you get f'(3)
and take the lim h->0

(b) just take the slope:
[f(7)-f(3)]/(7-3)

Answer 3

i did try that before posting the question, it gave a wrong answer.