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

Question

i am in deep need of help!

Answer 1

The curve is , and the point is .

We can use implicit differentiation to find y '.

The implicit(or total) derivation of is,

.

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

.

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

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

y = mx + b.

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

b = 1.

Substitute and b in y = mx + b.

y = (1 / 2)x + 1.

The tangent line equation is .