Let f, g : [–1, 2] → R be continuous function which are twice differentiable on the interval (–1, 2). Let the values of f and g at the points –1, 0 and 2 be as given in the following table :
In each of the intervals (–1, 0) and (0, 2) the function (f – 3g)" never vanishes. Then the correct statement(s) is (are) [JEE (Advanced) 2015]
Text Solution
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(b,c)Let h(x) = f(x) – 3g(x)
⇒ h'(x) = 0 has atleast one root in (–1, 0) and atleast one root in (0, 2)
h(2) = 3
But since h"(x) = 0 has no root in (–1, 0) & (0, 2) therefore h'(x) = 0 has exactly 1 root in (–1, 0) & exactly 1 root in (0, 2)
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