# How to find instantaneous rate of change for #y=4x^3+2x-3# at x=2?

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We can find the derivative using the power rule. Here, we multiply the constant times the exponent, and the power gets decremented. Doing this, we get

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To find the instantaneous rate of change of the function ( y = 4x^3 + 2x - 3 ) at ( x = 2 ), you need to find the derivative of the function ( y ) with respect to ( x ), which gives you the slope of the tangent line at ( x = 2 ). Then, substitute ( x = 2 ) into the derivative to find the instantaneous rate of change at that point.

Taking the derivative of ( y ) with respect to ( x ) gives:

( \frac{dy}{dx} = 12x^2 + 2 )

Now, substitute ( x = 2 ) into the derivative:

( \frac{dy}{dx} \bigg|_{x=2} = 12(2)^2 + 2 = 48 + 2 = 50 )

So, the instantaneous rate of change of ( y = 4x^3 + 2x - 3 ) at ( x = 2 ) is ( 50 ).

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