Posted by **catherine** on Tuesday, September 14, 2010 at 10:02pm.

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.

- calculus -
**TutorCat**, Tuesday, September 14, 2010 at 10:29pm
please show your work. maybe myself or the other tutors could figure out what you did wrong.

- calculus -
**catherine**, Tuesday, September 14, 2010 at 10:35pm
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...

- calculus -
**MathMate**, Tuesday, September 14, 2010 at 10:56pm
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.

- calculus -corr -
**MathMate**, Tuesday, September 14, 2010 at 11:01pm
Sorry, the equation should read:

f(3+h) = 9h^2 + 8h + f (3)

- calculus -corr² -
**MathMate**, Tuesday, September 14, 2010 at 11:06pm
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=?

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