What is the instantaneous rate of change for $f (x) = x^{3} - x^{2} - 2 x 4$ $f(x)=x^3-x^2-2x 4$ when x=2?

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Answer 1 · 2018-06-13T21:16:33

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The instantaneous rate of change is the gradient of the slope at a given point, in this case, when $x = 2$ $x=2$

The function is: $f (x) = x^{3} - x^{2} - 8 x$ $f(x)=x^{3}-x^{2}-8x$

The gradient function is: $f'(x)=3x^{2}-2x-8$

Let $x=2$

therefore the gradient of the curve at this point is

$f'(x)=3*4-2*2-8$
$f'(x)=12-4-8$
$f'(x)=0$

What is the instantaneous rate of change for f(x)=x^3-x^2-2x 4f(x)=x3−x2−2x4f(x)=x^3-x^2-2x 4 when x=2?