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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).

For strictly increasing function f'(x) >0 for given interval For strictly decreasing function f'(x) <0 for given interval Here f'(x) =2x-1 interval (-1, 1) at x= - 1/2 , f'(x) = -2 at x=3/4 , f'(x) = 1/2 Hence prove function neither strictly increasing nor strictly decreasing in given interval...

For strictly increasing function f'(x) >0 for given interval

For strictly decreasing function f'(x) <0 for given interval

Here

f'(x) =2x-1 interval (-1, 1)

at x= - 1/2 , f'(x) = -2

at x=3/4 , f'(x) = 1/2

Hence prove function neither  strictly increasing nor strictly decreasing in given interval (−1, 1).

Experienced and certified reaching for iit mains and advanced level having 20 years of experience

f'(X)=2x-1 is neither positive nor negative in (-1,1)

The given function is f(x) = x2 − x + 1. The pointdivides the interval (−1, 1) into two disjoint intervals i.e., Now, in interval Therefore, f is strictly decreasing in interval. However, in interval Therefore, f is strictly increasing in interval. Hence, f is neither strictly increasing...

The given function is f(x) = x2x + 1.

The pointdivides the interval (−1, 1) into two disjoint intervals i.e.,

Now, in interval

Therefore, f is strictly decreasing in interval.

However, in interval

Therefore, f is strictly increasing in interval.

Hence, f is neither strictly increasing nor decreasing in interval (−1, 1).

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