Let f : a , b → R be twice differentiable function such that f x = ∫ a x g t d t for a differentiable function g x . If f x = 0 has exactly five distinct roots in a , b , then g x g ' x = 0 has at least :

Question

Let f : a , b &#8594; R be twice differentiable function such that f x = &#8747; a x g t d t for a differentiable function g x . If f x = 0 has exactly five distinct roots in a , b , then g x g ' x = 0 has at least :

Quantrex Academy · Accepted Answer

Correct answer: C. seven roots in a , b

Let f : a , b &#8594; R be twice differentiable function such that f x = &#8747; a x g t d t for a differentiable function g x , Now, f x = &#8747; a x g t d t Since, f x has 5 roots and f ' x has atleast 4 roots g x has atleast 4 roots Therefore, g ' x has atleast 3 roots. Hence, g x g ' x has atleast 7 roots.

Let f : a , b → R be twice differentiable function such that f x = ∫ a x g t d t for a differentiable function g x . If f x = 0 has exactly five distinct roots in a , b , then g x g ' x = 0 has at least :

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More from Application of Derivatives

Let f : a , b &#8594; R be twice differentiable function such that f x = &#8747; a x g t d t for a differentiable function g x . If f x = 0 has exactly five distinct roots in a , b , then g x g &#39; x = 0 has at least :

Options

Correct answer

Step-by-step solution

More from Application of Derivatives

Let f : a , b → R be twice differentiable function such that f x = ∫ a x g t d t for a differentiable function g x . If f x = 0 has exactly five distinct roots in a , b , then g x g ' x = 0 has at least :