Thread: I need help in my online calculus class.

The example online states that:
The line x=c (where c>0) intersects the cubic y1=(2x^3)+(3x^2)-9 at point P and the parabola y2=(4x^2)+4x+5 at point Q.
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.
b) Write the equation of the two tangent lines described in part a.

I am taking this course online, so I don't have a formal instructor who I can ask questions to. If someone could explain to me what I am supposed to be doing, or even showing me the steps, that would be great. It is in a review section, so I have no idea what topic or chapter I am supposed to be using. All i know is that I should be using derivatives to find the tangent lines. Thanks.

Originally Posted by macroecon

The example online states that:
The line x=c (where c>0) intersects the cubic y1=(2x^3)+(3x^2)-9 at point P and the parabola y2=(4x^2)+4x+5 at point Q.
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.
b) Write the equation of the two tangent lines described in part a.

I am taking this course online, so I don't have a formal instructor who I can ask questions to. If someone could explain to me what I am supposed to be doing, or even showing me the steps, that would be great. It is in a review section, so I have no idea what topic or chapter I am supposed to be using. All i know is that I should be using derivatives to find the tangent lines. Thanks.

Two tangents are parallel iff their slopes are equal. For a), you want to find the value of c such that the derivative of y1 at c equals the derivative of y2 at c. For b), note that a line passing through a point (p, q) with slope m is given by y = m(x - p) + q.