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} = 3

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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: $\frac{dy}{dx} = 0$. Setting the derivative to zero: $3x^2 - 6x - 9 = 0$. Dividing by $3$: $x^2 - 2x - 3 = 0$. Factoring the quadratic equation: $(x - 3)(x + 1) = 0$. Thus,the 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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