Find the average rate of change of f(x)=x^2-3x-3 from x to h and what is the instantaneous change?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The average rate of change of a function f(x) from x = a to x = b is given by (f(b) - f(a))/(b - a). The instantaneous change is the derivative of the function f'(x)

Here, f(x) = x^2-3x-3

The average change from x to h is

[f(h) - f(x)]/(h - x)

=>[h^2-3h-3-x^2+3x+3]/(x - h)

=> [h^2-x^2-3h+3x]/(x - h)

=> [(h-x)(h+x)-3(h-x)]/(x - h)

=> 3 - (h + x)

The instantaneous change of f(x) is f'(x) = 2x - 3

The average change from x to h is 3 - (h + x). And the instantaneous change is f'(x) = 2x - 3

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