Cubic Inequalities
Akopọ
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.
Awọn Afojusun
- Solve graphically cubic inequalities of the form f(x) > d, f(x) >= d, f(x) < d or f(x) <= d, where f(x) is a product of three linear factors and d is a constant.
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Oriire fun ipari ẹkọ lori Cubic Inequalities. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
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- 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
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