1.

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?

Answer»

Solution :(a) The graph ofy = 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) Asf(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, forallx,` so f(x) is always decreasing.


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