January 9th, 2014, 06:20 AM  #1 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  Gradient function.
The gradient function of a curve is px^2qx, 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 xcoordinate =1 is 8. Find the values of p and q , The equation of the curve 
January 9th, 2014, 12:51 PM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  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 xcoordinate =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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