# Thread: solving with 3 variables: Given clues

1. ## 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!

Mike

2. Originally Posted by mike_302
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!

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 $\frac{dy}{dx} = ac(ax + b)^{c-1} = 18$

3. 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

4. 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.