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Math Help - solving with 3 variables: Given clues

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    solving with 3 variables: Given clues

    I don't even know where to begin on this question! It's grade 12 calculus. We just finished learning the chain rule.

    25. The graph of y=(ax+b)^c, where a,b,c are real constants, has a tangent line at (3,27) defined by y=18x-135. The graph also has a point of inflection, (-1.5, 0). Determine a, b, c.


    At the very least, help me to get started by solving for one of these variables!

    Please and thank you.

    Mike
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    Quote Originally Posted by mike_302 View Post
    I don't even know where to begin on this question! It's grade 12 calculus. We just finished learning the chain rule.

    25. The graph of y=(ax+b)^c, where a,b,c are real constants, has a tangent line at (3,27) defined by y=18x-135. The graph also has a point of inflection, (-1.5, 0). Determine a, b, c.


    At the very least, help me to get started by solving for one of these variables!

    Please and thank you.

    Mike
    Is it a stationary point of inflexion or just a point of inflexion?

    Hint: The tangent line has the same gradient as the curve at the point (3, 27).

    So \frac{dy}{dx} = ac(ax + b)^{c-1} = 18
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    yes, I got that far. And then I had subbed 3 into x. But at that point, I still have 3 variables and one equation... At grade 12 calculus, at the very BEST of times, the most we have ever been taught/can do is solve for 2 variables by subbing one equation into another. I have no diea how to deal with all 3 variables here. :S
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  4. #4
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    OH! here's something I just worked out... a factor of the function must be (2x+3)

    And that factor would also have to be a factor of the second derivative.
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