Question

: Find the equation of the tangent line to the curve f(x)= e^xat x_0= 2, and show this line on the graph.

Answer 1

The tangent line to f(x) = e ˣ at the point x = 2 has slope equal to f ' (2):

f(x) = e ˣ → f '(x) = e ˣ → f ' (2) = e ²

At x = 2, the function takes on a value of f (2) = e ². Use the point-slope formula to get the equation of the tangent line:

y - e ² = e ² (x - 2)

Solve for y :

y = e ² x - e ²