How do you find the equation of the tangent line to the graph #f(x)=e^(1-x)# through point (1,1)?

Question

2057 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-10T17:37:41

The tangent line is: #y=2-x#

The equation of the tangent line to the curve #y=f(x)# in the point #(bar x, f(bar x))# is given by the formula:

#y=f(barx)+f'(barx)(x-barx)#

In our case:

#f(x) = e^(1-x) => f(1) = 1#

#f'(x) = -e^(1-x) => f'(1) = -1#

So the tangent line is:

#y=1-(x-1)=2-x#

enter image source here