How to find instantaneous rate of change for y=4x3+2x−3 at x=2?

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Davon Friedman · Accepted Answer

Explanation:We need to differentiate the expression, 4x3+2x−3 to find the slope of the tangent, ddx[4x3+2x−3]=12x2+2, [by the general power rule for differentiation, i.e, if  y=axn,dydx=anxn−1]and so when x=2, dydx=12[2]2+2=50.This is the rate of change of y with respect to x at the point where x=2, and means y is changing fifty times faster than x at this point. Hope this was helpful.

Eliza Flores · Accepted Answer

&quot;Instantaneous rate of change&quot; is just a fancy way of saying &quot;derivative&quot;. We need to differentiate this business and plug in 2 at the end.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 gety′=12x2+2NOTE: Recall that the derivative of an x term is just its coefficient, and the derivative of a constant is 0.Now, we can plug 2 in for x to get=12(2)2+2=48+2=50The instantaneous rate of change at x=2 is 50.

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

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