Question

How do you sketch the curve `y=e^x-sinx` by finding local maximum, minimum, inflection points, asymptotes, and intercepts?

Answer 1

Identify those critical points from the first and second derivatives of the function. Then you can "sketch" the curve knowing the basic shape.

Explanation:

The first derivative will identify inflection points. The second derivative will show their direction. Intercepts are "solutions = where `y = 0` and asymptotes are either points where the function becomes infinite or is undefined.

See the following reference for details in calculation and interpretation:
Weisstein, Eric W. "First Derivative Test." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/FirstDerivativeTest.html
Weisstein, Eric W. "Second Derivative Test." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SecondDerivativeTest.html