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Prove that the function f given by f(x) = x2 − x + 1 is neither strictly increasing nor strictly decreasing on (−1, 1). - Mathematics

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प्रश्न

Prove that the function f given by f(x) = x2 − x + 1 is neither strictly increasing nor strictly decreasing on (−1, 1).

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उत्तर

f(x) = x2 - x + 1

f'(x) = 2x - 1

if,  f'(x) = 0

2x - 1 = 0

x = `1/2`

x = `1/2` is divided into the intervals (-1, 1), `(-1, 1/2), (1/2, 1)`.

Hence, the function is neither increasing nor decreasing in (-1, 1).

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Application of Derivatives - Exercise 6.2 [पृष्ठ २०६]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 6 Application of Derivatives
Exercise 6.2 | Q 11 | पृष्ठ २०६

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