Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let a function 
be defined as :
where 
. If / is continuous at x = 4, then which of the following statements is NOT true ?
A
is not differentiable at x = 4
B
'(3) + 
'(5) = 
C
is increasing in 
D
has a local minima at x = 
Text Solution
Verified by ExpertsThe correct answer is:
C
Given 
f(x) is continuous at x = 4
So 
So 
16 + 4b = 15
So 
At x = 4
LHD 
RHD = 5-|x-3|=4
LHD 
RHD
Option is true
and f (3) + f (5) = 
+ 3 = 
Option is true
at 
This function is not increasing.
In the interval in 
Option is NOT TRUE.
This function f(x) is also local minima at x = 
──────────────────────────────────────────────────────────────────────────────────────────
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
The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If i…
f(x) = 4 log e (x - 1) -2x 2 + 4x +5, x > 1, which one of the following is NOT correct ?
the tangent at the point (x 1 ,y 1 ) on the curve y = x 3 +3x 2 + 5 passes through the origin, then…
The sum of absolute maximum and absolute minimum values of the function f(x) = |2x 2 + 3x – 2| + si…
The number of distinct real roots of the equation x 2 -7x-2 = 0 is
Let be the largest value of , for which the function is increasing for all . Then is equal to :