Find the equation of the tangent line to f(x) = x^2 + 2x at x = 1.

Step 1: Find the point on the curve.

The function is:
f(x) = x^2 + 2x

Evaluate f(1):
f(1) = 1^2 + 2(1)
f(1) = 1 + 2
f(1) = 3

So the tangent line passes through the point (1, 3).

Step 2: Find the derivative.

Differentiate:
f'(x) = 2x + 2

The derivative gives the slope of the tangent line at any x-value.

Step 3: Find the slope at x = 1.

f'(1) = 2(1) + 2
f'(1) = 4

So the tangent line has slope 4.

Step 4: Use point-slope form.

The point-slope equation is:
y - y1 = m(x - x1)

Substitute m = 4 and the point (1, 3):
y - 3 = 4(x - 1)

Step 5: Simplify.

y - 3 = 4x - 4

y = 4x - 1

Therefore, the equation of the tangent line is y = 4x - 1.