Suppose for a function y = f(x) that f(-2) = 3 and f'(-2) = 23 . write the equation of the tangent line to f(x) at x = -2.

The equation of tangent line is .

Step-by-step explanation:

Given information: y = f(x) that f(-2) = 3 and f'(-2) = 23 .

The given function is

Differentiate with respect to x.

We need to find the equation of the tangent line to f(x) at x = -2.

Slope of tangent line is

Slope of line is 23.

At x=-2 the value of function is 3. It means the tangent line passes through the point (-2,3).

Equation of tangent line is

Add 3 on both sides.

Therefore the equation of tangent line is .