Let ƒ : [a; b] → R be a continuous function and let F(x) = f(t)dt where x > a. (a) Show that if f is increasing, then F(x) ≤ f(x)(x − a). (b) Use the continuity of f to show that F'(x) = f(x). (c) Explain why F is also continuous. a
Let ƒ : [a; b] → R be a continuous function and let F(x) = f(t)dt where x > a. (a) Show that if f is increasing, then F(x) ≤ f(x)(x − a). (b) Use the continuity of f to show that F'(x) = f(x). (c) Explain why F is also continuous. a
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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