The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)-9 at point P and the parabola y=4x^(2)+4x+5 at point Q.

Question

a. If a line tangent to the cubic at point P is parallel to the line tangent to the parabola at point Q, find the value of c where c>0.

Answer 1

Find the derivative fc(x) of the cubic, and fp(x) of the parabola.

By equating fc(x) and fp(x), we can find the value of x for which their tangents have the same slopes.

If I am not mistaken, c=1.