How do you find the equation of the tangent line to the graph of #f(x)=x+4/x# at point (4,5)?
1 Answer
Feb 9, 2017
The tangent line will be:
Explanation:
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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.
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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.)
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To get slope, you need to do the 1st derivative of the f(x), which is
#f'(x) = 1-4/x^2# -
Pluggin the point (4,5) and you will get the slope of the tangent line,
#slope = f'(4) = 3/4# -
Now you have a point and a slope, the line can be easily determined.