Write the equation of the tangent to the graph of the function f (x) = e ^ x at the point with the abscissa x0 = -1.

In general, the tangent equation is: y = (f (x0)) ‘* x + b.

Let’s find the derivative of the function:

y ‘= (e ^ x)’ = e ^ x.

y ‘(- 1) = e ^ (- 1) = 1 / e.

Find the value of the function at a given point:

y (-1) = e ^ (- 1) = 1 / e.

Since the point of tangency is common, we get the equation for b:

1 / e * (-1) + b = 1 / e;

b = 0.

Answer: the required equation of the tangent line at the point x0 = -1 has the form y = 1 / e * x.