SOLUTION: The curve for which dy/dx=a(x-p)(x-q) where a,p,q are constants, has turning point at (2,0) and (1,1) Determine the value of a using the information above.

Algebra ->  Exponents -> SOLUTION: The curve for which dy/dx=a(x-p)(x-q) where a,p,q are constants, has turning point at (2,0) and (1,1) Determine the value of a using the information above.      Log On


   

Question 1044081: The curve for which dy/dx=a(x-p)(x-q) where a,p,q are constants, has turning point at (2,0) and (1,1)
Determine the value of a using the information above.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Turning points of a curve are points where the derivative dy%2Fdx+=+0.
===> the derivative dy%2Fdx=a%28x-p%29%28x-q%29 is actually +dy%2Fdx=a%28x-2%29%28x-1%29,
and wouldn't matter whether p=2 and q=1, or p=1 and q=2.
===> +dy%2Fdx=a%28x-2%29%28x-1%29+=+a%28x%5E2-3x%2B2%29,
===> y+=+a%28x%5E3%2F3-3x%5E2%2F2%2B2x%29%2Bc, after getting the integral.
Plugging in the respective coordinates of the point (2,0) into the last equation gives
0+=+2a%2F3%2Bc. (Verify!)
Similarly, for the point (1,1), we get
1+=+5a%2F6+%2B+c. (Again verify!)
===> highlight%28a+=+6%29, c = -4, and the curve itself is
y+=+2x%5E3+-+9x%5E2+%2B+12x+-4.