For what value of xx is the slope of the tangent line to y=x^5 -x^2 +sinxy=x5x2+sinx undefined?

2 Answers
Aug 17, 2017

No real xx (the slope of the tangent line is well defined for all finite values of xx)

Explanation:

The slope of the tangent is given by

dy/dx = 5x^4-2x+cos xdydx=5x42x+cosx

As this is well defined for all finite values of xx the tangent line is well defined everywhere!

Aug 17, 2017

None

Explanation:

The slope of the tangent line to the graph of y = x^5-x^2+sinxy=x5x2+sinx at any point xx is given by

y' = 5x^4-2x+cosx

y' is defined for all x, so the slope of the tangent line is defined for all x