First slide

Mean value theorems

Question

$The real number k for which the equation, 2 x^{3} + 3 x + k = 0 has two distinct real roots in [0, 1]$

Moderate

A

lies between 1 and 2
B

Lies between 2 and 3
C

lies between -1 and 0
D

Does not exist

Solution

$clearly f^{'} (x) = (6 x^{2} + 3) > 0, f (x) is increasing function f (x) = 0 will have no$ $real roots in [0, 1]$

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