Question

How do you find the equation of the tangent line to the graph of `f(x)=x+4/x` at point (4,5)?

Answer 1

The tangent line will be: `y=3/4x+2`

Explanation:

1. First, to determine a line, you need two points or one point and one slope. In this case, you already get a point (4,5), then you need one more point or the slope of the tangent line.

2. Because the slope of the tangent line is easy to get, we will try obtain the slope. (Actually you cannot find another point on tangent line in this question.)

3. To get slope, you need to do the 1st derivative of the f(x), which is `f'(x) = 1-4/x^2`

4. Pluggin the point (4,5) and you will get the slope of the tangent line, `slope = f'(4) = 3/4`

5. Now you have a point and a slope, the line can be easily determined.