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

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Question

(A) The given curve is $y=3x^{4}-4x$.The slope of the tangent to the curve at any point $x$ is given by the derivative $\frac{dy}{dx}$.$\frac{dy}{dx}

Vedclass · Accepted Answer

$764$

Vedclass · Answer

(A) The given curve is $y=3x^{4}-4x$.The slope of the tangent to the curve at any point $x$ is given by the derivative $\frac{dy}{dx}$.$\frac{dy}{dx} = \frac{d}{dx}(3x^{4}-4x) = 12x^{3}-4$.To find the slope of the tangent at $x=4$,we substitute $x=4$ into the derivative:$\left(\frac{dy}{dx}\right)_{x=4} = 12(4)^{3}-4$.$= 12(64)-4$.$= 768-4 = 764$.Thus,the slope of the tangent at $x=4$ is $764$.

Find the slope of the tangent to the curve $y=3x^{4}-4x$ at $x=4$.

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