To calculate: The value of the function
Answer to Problem 50RE
The value of x equal to 0, y equal to 3
Explanation of Solution
Given information:
The given figures are shown below,
Formula used:
Calculation:
Correct option (b)
By fundamental theorem of calculus, part 1, it is given that-
If f is continuous on [ a, b ], then
Proof-
Apply the definition of the derivative directly to the function F . That is,
The expression in brackets in the last line is the average value of f from x to x + h : The mean value theorem for definite integrals. That f , being continuous, takes on its average value at least once in the interval; that is,
So,
As x + h gets closer to x , it carries c along with it like a bead on a wire, forcing c to approach x . Since f is continuous, this means that f (c) approaches f (x):
Putting it all together,
So,
Here,
Hence,
Observe the graphs drawn in the question, in the graph (b), at x equal to 0, y equal to 3.
Conclusion:
The value of x equal to 0, y equal to 3
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th Edition)
Calculus & Its Applications (14th Edition)
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