calculus

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.

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

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  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...

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  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.

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

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  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=?

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