Calculus Derivatives

Question

Find an equation for the tangent line to the graph of

f(x) = x + sinx - 1

at (0, f(0))

Answer 1

First, let's find the point that the line goes through. the x is 0, the y is f(0) or 0 + sin(0) - 1 = 0 + 0 - 1 = -1. So the point is (0, -1).

The equation of the line can be written in slope-intercept form as y = mx + b. In this case, the point in question (0, -1) IS the y-intercept so b = -1. The slope (m) is the derivative of the function evaluated at x = 0.

The derivative of f(x) = x + sinx - 1 is f '(x) = x' + (sin(x))' - 1' = 1 + cos(x) - 0 = 1 + cos(x) and f '(0) = 1 + cos(0) = 1 + 1 = 2

So the equation of the line is y = 2x - 1