Paragraph: Let F : R → R be a thrice differentiable function. Suppose that F ( 1 ) = 0 , F ( 3 ) = − 4 and F ′ ( x )

Question

Paragraph: Let F : R → R be a thrice differentiable function. Suppose that F ( 1 ) = 0 , F ( 3 ) = − 4 and F ′ ( x ) < 0 for all x ∈ ( 1/2 , 3 ) . Let f ( x ) = x F ( x ) for all x ∈ R . Question: The correct statement(s) is(are)

TestHub · Accepted Answer

F 1 = 0 , F 3 = - 4 F ′ x < 0 F ( x ) is decreasing, also F x < 0 Now, f x = x F ( x ) x ∈ 1 2 , 3 x F x < 0 ∴ f 2 < 0 Also, f ′ x = x F ′ x + F ( x ) f ′ 1 = F ′ 1 < 0 Also, f ( x ) is strictly decreasing Now, F 1 = F x = 0 ∴ f ′ x ≠ 0 a s F ′ x < 0 a n d f x is decreasing.

Mathematics - Application of Derivative Question with Solution | TestHub

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