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Question

The abscissa of the points of the curve y=x3 in the interval [–2, 2], where the slope of the tangents can be obtained by mean value theorem for the interval [–2, 2], are
[MP PET 1993]

A
±23
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B
± 3
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C
±32
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D
\N
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Solution

The correct option is A ±23
According to the mean value theorem,
f'(c) = f(b)f(a)ba in the interval [a,b]
f'(c) = f(8)f(8)8+8
f'(c) = 4
Also, f'(c) = 3c2
so, 3c2 = 4
or c = ±23

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