First slide

Mean value theorems

Question

Rolle’s theorem holds for the function $x^{3} + b x^{2} + c x, 1 \leq x \leq 2$ at the point $\frac{4}{3}$ , the value of $b$ and $c$ are

Moderate

A

$b = 8, c = - 5$
B

$b = - 5, c = 8$
C

$b = 5, c = - 8$
D

$b = - 5, c = - 8$

Solution

Here $f (1) = f (2)$ and $f' (\frac{4}{3}) = 0$
$\Rightarrow 1 + b + c = 8 + 4 b + 2 c$ and
$3 {(\frac{4}{3})}^{2} + 2 b (\frac{4}{3}) + c = 0 16 + 8 b + 3 c = 0 7 + 3 b + c = 0 s o l v i n g e q a t i o n s (b, c) = (- 5, 8)$ .

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