The abscissae of the points,where the tangent | vedclass

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(D) Given the curve equation: $y=x^{3}-3x^{2}-9x+5$. To find the slope of the tangent,we differentiate $y$ with respect to $x$: $\frac{dy}{dx} = 3x^{2

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$x=-1$ and $3$

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(D) Given the curve equation: $y=x^{3}-3x^{2}-9x+5$. To find the slope of the tangent,we differentiate $y$ with respect to $x$: $\frac{dy}{dx} = 3x^{2}-6x-9$. Since the tangent is parallel to the $x$-axis,its slope must be zero: $\frac{dy}{dx} = 0$. Substituting the derivative: $3x^{2}-6x-9 = 0$. Dividing by $3$: $x^{2}-2x-3 = 0$. Factoring the quadratic equation: $(x-3)(x+1) = 0$. Thus,the values of $x$ (abscissae) are $x=3$ and $x=-1$.

The abscissae of the points,where the tangent to the curve $y=x^{3}-3x^{2}-9x+5$ is parallel to the $x$-axis,are

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