How do you find the instantaneous rate of change of y with respect to x at an arbitrary value of $X_o$ if $y=2x^2$ and $X_o=0$ ?

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Answer 1 · 2015-04-06T01:19:40

If $y=f(x)=2x^2$ , then by the power rule, the instantaneous rate of change of $y$ with respect to $x$ is the derivative $dy/dx=f'(x)=4x$ .

At an arbitrary point $x=X_{0}$ , this derivative is just $f'(X_{0})=4X_{0}$ . If $X_{0}=0$ , then $f'(X_{0})=f'(0)=4\cdot 0=0$ .

How do you find the instantaneous rate of change of y with respect to x at an arbitrary value of X_oX_o if y=2x^2y=2x^2 and X_o=0X_o=0?