Find the instantaneous rate of change of y with respect to x at x₀ = 4. y = 4x² - 8

Question

Quizplus · Accepted Answer

The instantaneous rate of change of $y$ with respect to $x$ is given by the derivative of $y$ with respect to $x$. For $y = 4x^{12} - 8$, the derivative is $dy/dx = 48x^{11}$. Substituting $x = 4$ into this derivative gives $48(4)^{11} = 48 \times 4^{11} = 48 \times 2^{22}$. Simplifying this, we find that $48 \times 2^{22}$ equals $32$, which is the instantaneous rate of change at $x = 4$.

Find the Instantaneous Rate of Change of Y with Respect