The graph of derivative of a function f(x) is given as below and the graph represents an even function. Also let f(0) = 0,
and f(x) is not defined for any x, which satisfies |x| > a. Now answer the followings.
(i) The function f(x) is
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Ans.
(i)
Sol. Derivative of odd function will be even function f(x) = – f(–x) → f(x) odd
f '(x) = + f '(–x) → f '(x) even
Clearly f '(x) is even then f(x) will be odd.
(ii)
Sol. Clearly from graph lies below the x axis f '(x) < 0 then f(x) will be decreasing function.
(iii)
Sol. Domain of f '(x) = [–a, a] It means function is continuous in [–a, a] Domain of f(x) = [–a, a]
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