Following is the graph of y = f'(x) and f(0) = 0 . (a) What type of function y = f'(x) is ? Odd or even? (b) What type of function y = f(x) is ? Odd or even? (c) What is the value of `int_(-a)^(a) f(x) dx`? (d) Has y = f(x) point of inflection? (e) What is the nature of y = f(x)? Monotonic or non-monotonic?
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(a) The graph of y = f'(x) is symmetrical about the y-axis, so f(x) is an even function. (b) f(0) = 0, so f(x) is an odd function [derivative of an odd function is even]. (c) As f(x) is odd, so `underset(-a)overset(a) int f(x) dx = 0` (d) `f''(x) gt 0 as x lt 0 and f''(x) lt 0 "as " x gt 0`. Therefore, x = 0 is the point of inflexion. (e) ` f'(x) le 0, forall x, ` so f(x) is always decreasing.
The graph above shows the function y=f(x) over the interval 0lexle7 . What is the value of f(f(6)) ?
The graph of y=f(x) is given above. For what value of x is y=f(x-4) undefined?
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If the graph of the function y = f(x) is as shown : The graph of y = 1//2(|f(x)|-f(x)) is
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CENGAGE ENGLISH-GETTING STARTED WITH GRAPHS-Exercises 1.18
