1. The Mean Value Theorem is used to prove the First Fundamental
Theorem of Calculus.
What is the Mean Value Theorem (provide statement).
2. On the sketch below estimate the c for the Mean Value Theorem for the interval [a,b] = [1,4]. Support your answer by drawing the appropriate tangent line at your c and the appropriate secant line.
3. The Mean Value Theorem for Integrals is used to prove the Second Fundamental Theorem of Calculus.
The Mean Value Theorem for Integrals states that if f is
continuous on the closed interval [a,b] then there exists a
number c in the closed interval [a,b] such that (complete
the statement)
4. Estimate what the c in the Mean Value
Theorem for Integrals would be for the function f(x)
whose graph is below with the interval of integration being [1,4].
Sketch the appropriate rectangle on the graph to support your answer.
