Published by:
CGP EDU Academic Team
Published on: August 11, 2026
If f(x) be a twice differentiable function such that f(x) = x 2 for x = 1, 2, 3, the
Text Solution
Verified by ExpertsThe correct answer is:
B
Let g(x) = f(x) – x 2
⇒ g(x) has atleast 3 real roots which are x = 1,2,3
By langrange mean value theorem (LMVT)
⇒ g ′ (x) has atleast 2 real roots in x ∈ (1, 3)
⇒ g ′′ (x) has atleast 1 real roots in x ∈ (1, 3)
⇒ f ′′ (x) – 2 = 0 for atleast 1 real roots in x ∈ (1, 3)
⇒ f ′′ (x) = 2 for atleast one x ∈ (1, 3)
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If f(x) = cos π x + 10x + 3x 2 + x 3 , – 2 ≤ x ≤ 3 then absolute minimum value of f(x) is-
The function f(x) = x 5 – 5x 4 + 5x 3 – 1 has-
The function f(x) = has no extrema. if (n ∈ z)
If x exceeds by its square by the greatest possible quantity then x is-
An extreme value of the function
f(x) = (sin –1 x) 3 + (cos –1 x) 3 (–1 < x < 1) is
Let f(x) = (t + 4) 4 log (t+ 1) dt, then -