Question

Calculus Question:
x^2 + 2y^3 = 9.
a. Find (d^2y/dx^2) *second derivative*
b. the equation of the normal line to the curve at (3,0).

Answer 1

What's the first derivative?

Answer 2

-2x/6y^2 simplified to -x/y^2

Answer 3

I don't know how to find the second derivative though.

Answer 4

take the derivative of the first derivative to get the second derivative

Answer 5

would I take it of the simplified form then?

Answer 6

Either or would give you the same answer. To make sure that you did it right, try taking the derivative of both to see if you get the same answer.

Answer 7

oh got it thank you!
Do you know how to find the normal line?

Answer 8

You forgot the '3' in the denominator of the derivative.

Answer 9

Do you know what the definition of a normal line is? And what jam333 said ;)

Answer 10

The first derivative simplifies to -x/(3y^2). You just left out the 3.

Answer 11

Oh no wonder my second derivative was odd.
My notes said the normal line is perpendicular to the tangent line, but I forgot how to find it.

Answer 12

Find the perpendicular line, then take the reciprocal of the slope, using the point slope formula with the point that you were provided.

Answer 13

Sub x = 3 and y = 0 into the equation of the first derivative. That will give you the slope of the tangent line there. For the normal line, it will have a slope that is the NEGATIVE reciprocal. (I think.) Then you'll have a slope and a point so you can get the equation of the normal line.

Answer 14

Thank you guys! My computer lost connection from this site a while back. I figured out the problem now. Thank you so much!