Let f(x) = 8x^3 - 6x^2 - 2x + 1, then

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5. Continuity and Differentiation

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Let $f(x) = 8x^3 - 6x^2 - 2x + 1,$ then

A

$f(x) = 0$ has no root in $(0,1)$

B

$f(x) = 0$ has at least one root in $(0,1)$

C

$f' (c)$ vanishes for some $c\, \in \,(0,1)$

D

Both $(B)$ and $(C)$

Solution

Consider $g(x)$ which is the integral of $f(x)$ and apply Rolle’s theorem in it

$\int\limits_0^1 {f(x)dx} = 0$

==>$f (x) = 0$ has at least one root

Standard 12

Mathematics

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