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

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Answer 1 · 2017-08-17T13:21:15

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

The slope of the tangent is given by

$\frac{d y}{d x} = 5 x^{4} - 2 x + cos x$ $dy/dx = 5x^4-2x+cos x$

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

Answer 2 · 2017-08-17T13:23:18

None

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

For what value of xxx is the slope of the tangent line to y=x^5 -x^2 +sinxy=x5−x2+sinxy=x^5 -x^2 +sinx undefined?