Mathematics 1 Deneme Sınavı Sorusu #1357108
If f(x) is differentiable on an interval I,
I. f '(x) < 0 for all x ? (a, b) then f(x) is called monotone increasing
II. f '(x) > 0 is satisfied for all x ? (a, b) then f(x) is called monotone increasing
III. f '(x) > 0 is satisfied for all x ? (a, b) then f(x) is called monotone decreasing
IV. f '(x) < 0 for all x ? (a, b) then f(x) is called monotone decreasing
which of the given statements is true about monotonicity?
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I and II |
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I and III |
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I and IV |
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I, II and III |
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I, II and IV |
The monotonicity property of a function can be investigated by the sign of the derivative. If the
inequality f '(x) > 0 is satisfied for all x ? (a, b) then f(x) is called monotone increasing on the
interval (a, b); likewise, if f '(x) < 0 for all x ? (a, b) then f(x) is called monotone decreasing on
the interval (a, b). The answer is C.
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