Find the slope of the tangent to the graph of the function y = x-Inx at its point with the abscissa x = 3.
| September 2, 2021 | education
The slope is the value of the derivative at the tangent point. Therefore, the problem is reduced to finding this derivative and its value at the point x = 3.
We find the derivative of the given function, we get:
y ‘(x) = (x – ln x)’ = 1 – 1 / x.
By hypothesis, we find y ‘(3), i.e. we get:
y ‘(3) = 1 – 1/3 = 2/3.
Answer: The slope is 2/3.
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