Calculus Help

[Mr Smiley]

This is a tough one for you guys:
The line x=c where c>0 intersects the cubic y=2x^3+3x^2-9 at point P and the parabloa y=4x^2+4x+5 at point Q.
First Question: If a line tangent to the cubic at Point P is parrallel to the line tangent to the parabola at Point Q, find the value of c where c>0.
Second: Write the equations of the two tangent lines described in the first question.
😕
Any clue how I can start this?

 

[tfinch2]

tough?

People on this board could probably solve that with their eyes closed.

 

[CraKaJaX]

x=c

 

[VTHodge]

The slope of the tangent line is equal to the derivative of the equation evaluated at the point.

The tangent lines are parallel so they have the same slope.

First find the derivative of both equations, then solve for a value of X where the two expressions are equal.

 

[chuckywang]

1) c=1

2) y=12x+2, y=12x+1

 

[Mr Smiley]

Originally posted by: VTHodge
The slope of the tangent line is equal to the derivative of the equation evaluated at the point.

The tangent lines are parallel so they have the same slope.

First find the derivative of both equations, then solve for a value of X where the two expressions are equal.

Brilliant!

Originally posted by: chuckywang
1) c=1

2) y=12x+2, y=12x+1

Ok, I got the answer to number one but I don't understand how you made the equations for the second problem.

 

[chuckywang]

Originally posted by: Mr Smiley

Originally posted by: VTHodge
The slope of the tangent line is equal to the derivative of the equation evaluated at the point.

The tangent lines are parallel so they have the same slope.

First find the derivative of both equations, then solve for a value of X where the two expressions are equal.

Brilliant!

Originally posted by: chuckywang
1) c=1

2) y=12x+2, y=12x+1

Ok, I got the answer to number one but I don't understand how you made the equations for the second problem.

Regarding the tangent lines, you know the slope (from the derivative) and one point (either P or Q depending on which line). That is enough to determine the equation.

 

[VTHodge]

Originally posted by: Mr Smiley

Originally posted by: VTHodge
The slope of the tangent line is equal to the derivative of the equation evaluated at the point.

The tangent lines are parallel so they have the same slope.

First find the derivative of both equations, then solve for a value of X where the two expressions are equal.

Brilliant!

Thanks! Glad to help the next generation. 🙂

 

[FelixDeCat]

Dont forget to carry the one. Oh! And do your own homework. 🙂

 

[DrPizza]

Gee, thanks. That'll make a great problem for my poor students next week. 🙂