Calculus

Differentiability

Approximate Rate of Change

         

What is the average rate of change of the function f(x)=6x2+px+qf(x)=6x^2+px+q on the interval [a,b]?[a,b] ?

Given the symmetric difference quotient, f(a)f(a+h)f(ah)2h,f'(a) \approx \frac{f(a+h)-f(a-h)}{2h}, approximate f(2)f'(2) using the symmetric difference quotient for the function f(x)=x4f(x)=x^4 with h=0.04.h=0.04.

What is the average rate of change of the function y=2x2+7y=2x^2+7 when the value of xx changes from 55 to 7?7?

What is the slope of the secant line that passes through the two points (x,f(x))(x,f(x)) on the graph of the function f(x)=x2,f(x)=x^2, for x=2x=2 and x=2.004?x=2.004?

If f(x)=7x+3,f(x)=-7x+3, what is the average rate of change of f(x)f(x) when xx changes from 44 to 7?7?

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