Prove that the function x² – x + 1 is neither increasing nor decreasing on (0, 1).

Solution

Let $straight f left parenthesis straight x right parenthesis space equals space straight x squared minus straight x plus 1$
$straight f apostrophe left parenthesis straight x right parenthesis space equals space 2 straight x minus 1$
Now, $straight f apostrophe left parenthesis straight x right parenthesis space greater than space 0 space space space space for space space straight x greater than 1 half space space and space straight f apostrophe left parenthesis straight x right parenthesis space less than 0 space space for space straight x space less than space 1 half.$
$therefore space space space straight f left parenthesis straight x right parenthesis space is space increasing space in space open parentheses 1 half comma space 1 close parentheses space and space decreasing space in space open parentheses 0 comma space 1 half close parentheses therefore space space space space straight f left parenthesis straight x right parenthesis space is space neither space increasing space nor space decreasing space in space left parenthesis 0 comma space 1 right parenthesis$

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Application Of Derivatives

Prove that the function x² – x + 1 is neither increasing nor decreasing on (0, 1).

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

Prove that the function x2 – x + 1 is neither increasing nor decreasing on (0, 1).

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Prove that the function x² – x + 1 is neither increasing nor decreasing on (0, 1).