Work out an equation of the tangent line

Question

if a function f(x) has f(3)=2 and f'(3)=4, work out an equation of the tangent line to the graph of y=f(x) at the point (3, f(3))

Answer 1

The equation to the tangent line can be figured out as follows:

The tangent line is of the form y = mx + c. Now, m refers to the gradient of the tangent line. Since f'(3) = 4, the gradient of the tangent line passing through (3, f(3)) is 4. Hence m = 4. Thus, the equation to the tangent line is y = 4x + c. Now, we need to find the value of c. In order to do so, use the fact that the tangent line passes through (3, 2). We know this since f(3) = 2. Now, substituting x = 3 and y = 2, we get 2 = 4 * 3 + c which implies c = 2 - 4 * 3 = -10. Thus the equation to the tangent line is y = 4x - 10