Question

What is the equation of the tangent line of `f(x) =(e^(x^2)-x)(e^x-x^2)` at `x=2`?

Answer 1

`y=1159 x-2139`. See the illustrative tangent-inclusive Socratic graph.

Explanation:

f at x = 2= 178.26..

#f' = (e^(x^2)-x)(e^x-1)((2xe^(x^2)-1)(e^x-x)1159, nearly at x = 2.

So, the equation to the tangent is

y-178/26=1159(x-2)

graph{(y-1159x+2139)(y-(e^(x^2)-x)(e^x-x^2))=0 [-10, 10, -100 2200]}