What is the instantaneous rate of change of $f(x)=-2x^3+5 x^2+3x$ at $x=-2$ ?

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Answer 1 · 2017-06-15T21:42:09

$x=-41$

What you want to do first is find the derivative using the power rule.
The derivative is the instantaneous rate of change.

Which states:

$d/dxx^n=nx^(n-1)$

$d/dx=-(3)2x^(3-1)+(2)5x^(2-1)+(1)3x^(1-1)$

Please keep in mind that $x^(1-1)=x^0=1$

$d/dx=-6x^2+10x+3$

Now you plug in $x=-2$

$-6(-2)^2+10(-2)+3=-41$

What is the instantaneous rate of change of f(x)=-2x^3+5 x^2+3x f(x)=-2x^3+5 x^2+3x at x=-2x=-2?