Published by:
CGP EDU Academic Team
Published on: August 13, 2026
A function f(x) is defined in the interval [1, 4] as follows -
f(x) = log e [x], 1 ≤ x < 3
= |log e x|, 3 ≤ x < 4
The graph of the function f(x)
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,c)
f(x) = 0, 1 ≤ x < 2
= log e 2, 2 ≤ x < 3
= log e x, 3 ≤ x < 4
f(x) is continuous and differentiable everywhere except
perhaps at x = 2,3
f(2 – 0) = 0
f(3 – 0) = log 2
f(2 + 0) = log e 2
f(3 + 0) = log e 3
f(x) is not continuous at x = 2
f(x) is not continuous at x = 3
so graph broken at x = 2, 3
f(x) is not differentiable at x = 2, 3. The graph does not have a definite tangent at x = 2, 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 -