Find the slope of the tangent to the curve y | vedclass

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Question

(A) The slope of the tangent to the curve $y = f(x)$ at any point $x$ is given by the derivative $\frac{dy}{dx}$.Given the curve $y = x^{3} - x$.Diffe

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(A) The slope of the tangent to the curve $y = f(x)$ at any point $x$ is given by the derivative $\frac{dy}{dx}$.Given the curve $y = x^{3} - x$.Differentiating with respect to $x$,we get $\frac{dy}{dx} = 3x^{2} - 1$.To find the slope of the tangent at $x = 2$,we substitute $x = 2$ into the derivative:$\left. \frac{dy}{dx} \right|_{x=2} = 3(2)^{2} - 1 = 3(4) - 1 = 12 - 1 = 11$.Therefore,the slope of the tangent at $x = 2$ is $11$.

Find the slope of the tangent to the curve $y = x^{3} - x$ at $x = 2$.

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