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find the equation of the tangent line to the curve y=(2)/(1+e^-x) at the point (0,1)

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i am in deep need of help!

asked Feb 27, 2014 in CALCULUS by futai Scholar

1 Answer

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The curve is image, and the point is image.

We can use implicit differentiation to find y '.

The implicit(or total) derivation of image is,

image.

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

image

image.

This is the slope (m ) of the tangent line to the implicit curve at image.

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

y = mx + b.

1 = (1 / 2)(0) + b

b = 1.

Substitute image and b in y = mx + b.

y = (1 / 2)x + 1.

The tangent line equation is image.

answered Apr 10, 2014 by lilly Expert
edited Apr 10, 2014 by lilly

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