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Class XII Maths Applications of Derivatives 4

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Question 1

Rolle’s Theorem holds for the function f(x) = x³ + bx² + cx, 1 ≤ x ≤ 2 at the point $Description: Description: D:\GradeStack Courses\JEE Mains (Sent by Ravi)\JEE Mains Full Test\AIEEE-Full-Test-4-New_files\image313.png$ the value of b and c are

Question 2

If 2a + 3b + 6c =0, then at least one root of the equation

lies in the interval

Question 3

A value of C for which the conclusion of Mean value Theorem holds for the function f(x) = log_ex on the interval [1, 3] is

Question 4

Let f (x) be a polynomial function of second degree. If f (1) = f (−1) and a, b, c are in A. P., then f′ (a), f′ (b) and f′ (c) are in

Question 5

If f (x) = xⁿ, then the value of
f (1) −

Question 6

Let f be differentiable for all x. If f(1) = - 2 and f'(x) ≥ 2 for x ∈ [1, 6] , then

Question 7

Consider the function f(x) = |x – 2| + |x – 5|, x ∈ R.
Statement 1: f’(4) = 0
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5)

Question 8

A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to

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