Question

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

Answer 1

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

Explanation:

The slope of the tangent is given by

`dy/dx = 5x^4-2x+cos x`

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

Answer 2

None

Explanation:

The slope of the tangent line to the graph of `y = x^5-x^2+sinx` at any point `x` 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`