Name: nicholas
Who is asking: Student

Question:
the curve y= e^x(px^2+qx+r) is such that the tangents at x=1 and x=3 are parallel to the x-axis. the point (0,9) is on the curve. Find the values of p,q and r.

Hi Nicholas

Since the tangent lines at x=1 and x=3 are parallel to the x-axis the derivative of the function is zero at x=1 and x=3. If

Since f'(1) = 0 and f'(3) = 0, substituting x=1 and x=3 into f'(x) gives two equations in the variables p, q and r. (It is important here to remember tha e^x is not zero regardless of the value of x.)

The final condition you have is that f(0) = 9 which gives a third equation in the variables p, q and r. Now you should be able to solve for these variables.

Cheers,
Harley