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## Differentiability

Those friendly functions that don't contain breaks, bends or cusps are "differentiable". Take their derivative, or just infer some facts about them from the Mean Value Theorem.

# Approximate Rate of Change

What is the average rate of change of the function $$f(x)=6x^2+px+q$$ on the interval $$[a,b] ?$$

Given the symmetric difference quotient, $f'(a) \approx \frac{f(a+h)-f(a-h)}{2h},$ approximate $$f'(2)$$ using the symmetric difference quotient for the function $$f(x)=x^4$$ with $$h=0.04.$$

What is the average rate of change of the function $$y=2x^2+7$$ when the value of $$x$$ changes from $$5$$ to $$7?$$

What is the slope of the secant line that passes through the two points $$(x,f(x))$$ on the graph of the function $$f(x)=x^2,$$ for $$x=2$$ and $$x=2.004?$$

If $$f(x)=-7x+3,$$ what is the average rate of change of $$f(x)$$ when $$x$$ changes from $$4$$ to $$7?$$

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