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Calculus : Antiderivative and Rate of Change

36)If the functions f and g are defines for all real numbers and f is an antiderivative of g, which statements are not true?

I If g(x)>0 for all x, then f is increasing.
II If g(z)=0 then f(x) has a horizontal tangent at x+a.
III If f(x)=0 for all x, then g(x)=0 for all x.
IV If g(x)=0 for all x, then f(x)=0 for all x.
V F is continuous for all x.

Please tell why correct ones are correct.

35) What is the average rate of change of the function f defined by f(x)=a00*2^x on the interval [0,4]? Please give step by step explaination.

Solution Summary

An antiderivative is investigated and a rate of change is found.

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