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?

I and II

I and III

I and IV

I, II and III

I, II and IV

Yanıt Açıklaması:

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.

PAYLAŞ:

SORUNUN CEVABI: C

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