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Find an equation of the tangent line to the curve (x^2)(e^y)+(ye^x)=4 at the point (2,0).

0 votes

I think you're supposed to use implicit differentiation.

asked Feb 28, 2014 in CALCULUS by payton Apprentice

1 Answer

0 votes

The curve is image, and the point is (2, 0).

We can use implicit differentiation to find y '.

The implicit(or total) derivation of image is,

image

Substitute the values of (x, y ) = (2, 0) in the above equation.

image

image

image.

This is the slope (m ) of the tangent line to the implicit curve at (2, 0).

To find the tangent line equation, substitute the values of image and (x, y ) = (2,0) in the slope intercept form of an equation.

y = mx + b

image

image.

Substitute image and image in y = mx + b.

image

image.

The tangent line equation is image.

answered Apr 8, 2014 by lilly Expert

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