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.
... 0)=2〗 second fundamental theorem of calculus allows me ... by using any one of its infinitely many antiderivatives. in our case,the antiderivative we use is-cos ...
... integration questions and also explains optimization using calculus. ... Find the rate at which the distance between ... technique to find an antiderivative in terms ...
... a constant of integration after calculating the antiderivative. ... and the Fundamental Theorem of Calculus only when ... Suppose the rate of change of production of a ...
... of derivative, f ′( x ) represents the rate of change... 8. The Fundamental Theorem of Calculus provides an ... we only need to find the anti-derivative function b ...
... a method for computing slopes or rates of change... case, by the Fundamental Theorem of Calculus, integration and ... processes, ie (where F is an anti-derivative for f ...
... to time (remember that Newton invented calculus as a ... which is defined as the rate of change of ... a derivative is integration (also called anti-derivative). ...
... For Problems 55, 56 and 57, find an antiderivative F(x) with F'(x) = f(x) and F(0) = 5. ... Definite Integrals and Rate of Change are investigated ... Business Calculus. ...
