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Bayani Gaba-gaba

A cubic inequality asks where a cubic curve lies above or below a given level. The quickest reliable method is to sketch the curve from its factors and read off the intervals, rather than juggle algebra blindly.

In this lesson you will solve graphically cubic inequalities of the form \(f(x) > d\), \(f(x) \geqslant d\), \(f(x) < d\) or \(f(x) \leqslant d\), where \(f(x)\) is a product of three linear factors.

Nazarin Darasi

Barka da kammala darasi akan Cubic Inequalities. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.

Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.

Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.

The roots of (x + 2)(x - 1)(x - 3) = 0 are: A. 2, 1, 3 B. -2, 1, 3 C. -2, -1, -3 D. 2, -1, 3 Answer: B
Solve (x + 2)(x - 1)(x - 3) > 0. A. x < -2 or 1 < x < 3 B. -2 < x < 1 or x > 3 C. -2 < x < 3 D. x > 3 only Answer: B
At a simple root, a cubic graph: A. touches the axis B. crosses (changes sign) C. is undefined D. is flat Answer: B
For f(x) >= d (not strict), the roots are: A. excluded B. included C. ignored D. doubled Answer: B
The best first step for a cubic inequality is to: A. differentiate B. find roots and sketch C. integrate D. complete the square Answer: B