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January 9th, 2014, 06:20 AM   #1
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Gradient function.

The gradient function of a curve is px^2-qx, where p and q are constants. The curve has a turning point at (2,-. The gradient of the tangent to the curve at the point where its x-coordinate =-1 is 8.

Find the values of p and q ,

The equation of the curve
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January 9th, 2014, 12:51 PM   #2
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Re: Gradient function.

That's pretty straight forward, isn't it? "The gradient of the function is ".\
So the function itself is of the form for constants p, q, and c.

"The gradient of the tangent to the curve at the point where its x-coordinate =-1 is 8." Okay, the gradient is so we must have .

"The curve has a turning point at (2,-." That tells us two things. First when x= 2, y= -8 so . Also since it is a turning point, the derivative is 0: .

Solve those three equations for p, q, and c. It would probably be easiest to solve p+ q= 8 and 4p- 2q= 0 for p and q first, then solve the third equation for c.
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