Question

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



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

I am stuck on this one , tried every thing in the world. i don't know how to do it since there is no f(x) given.. so please be descriptive if you help. This is due tomorrow that's why i am posting it again, don't mean to spam.

Answer 1

please show your work. maybe myself or the other tutors could figure out what you did wrong.

Answer 2

ok. this question also had a part a) which was

(a) What is f '(3)?
so i just divided
(9h^2+8h)/h

(h(9h+8))/h and plugged in 0 since lim->0

got 8 as my answer.

now for B)

i tried plugging 3 into (h) in func 9h^2+8h/h

did same with 7 and got wrong answer. i tried many different ways but kept getting wrong answer.

what i am confused is with how to find values for f(7) and f(3) since there is no function given to begin with...

Answer 3

There is no limitation on the value/size of h, so h can be any number.

f (3 + h) - f (3) = 9h^2 + 8h
so
f(3+h) = 9h^2 + 8h - f (3)
Try setting h=4 to see what you get.

Answer 4

Sorry, the equation should read:
f(3+h) = 9h^2 + 8h + f (3)

Answer 5

In fact, the solution is simpler than that.
Remember TutorCat said:
for the secant:
[f(7)-f(3)]/(7-3)
you can work out
[f(7)-f(3)]
from
f (3 + h) - f (3) = 9h^2 + 8h
by putting h=?