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

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(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 equation $y = x^3 - x

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 equation $y = x^3 - x$.Differentiating both sides with respect to $x$,we get:$\frac{dy}{dx} = \frac{d}{dx}(x^3 - x) = 3x^2 - 1$.To find the slope of the tangent at $x = 2$,we evaluate the derivative at $x = 2$:$\left. \frac{dy}{dx} \right|_{x=2} = 3(2)^2 - 1$.$= 3(4) - 1$.$= 12 - 1 = 11$.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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