Question

Equation of a tangent line

Answer 1

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Answer 2

If you're given a function of x, along with a point on the graph, how do you find the slope of the tangent line at that point?

If you're given an implicit function, along with a point on the graph, how do you find the slope of the tangent line at that point?

Hint: apply implicit differentiation. Solve the resulting equation for dy/dx.

Answer 3

Implicitly differentiate the asteroid's equation. Solve for y', then evaluate it at x and y.

Answer 4

So far I have..
\[\LARGE \frac{2}{3}x^{-1/3}+\frac{2}{3}y^{-1/3}*y'=0\]

Answer 5

Solve for y'

Answer 6

Simplified..
\[\LARGE \frac{2}{3x^{1/3}}+\frac{2}{3y^{1/3}}*y'=0\]
\[\LARGE \frac{2}{3y^{1/3}}*y'=-\frac{2}{3x^{1/3}}\]
Multiply by the inverse?
\[\LARGE y'=\frac{y^{1/3}}{x^{1/3}}\]

Answer 7

*reciprocal

Answer 8

Yes.

Answer 9

Its only algebra. Don't let the notation scare you.