Home
Class 12
MATHS
Consider the function f(x)=|x-2|+|x-5|,x...

Consider the function `f(x)=|x-2|+|x-5|,x in RR`.
Statement-I : `f'(4)=0`.
Statement-II : f is continuous is [2, 5], differentiable in (2, 5) and `f(2)=f(5)`.

A

Statement-I is true, Statement-II is true, Statement-II is true, Statement-II is not a correct explanation for Statement-I.

B

Statement-I is true, Statement-II is false.

C

Statement-I is false, Statement-II is true.

D

Statement-I is true, Statement-II is true , Statement-II is a correct explanation for Statement-I.

Text Solution

Verified by Experts

Promotional Banner

Similar Questions

Explore conceptually related problems

Consider the function f(x) = |x-2|+|x-5|, Statement 1: f'(4)=0 Statement 2: differentiable in (2,5) and f(2)=f(5)

Show that the function f(x)=5x-|2x| is continuous at x = 0

Statement - I : If f(x) = sinx, then f'(0) = f'(2pi) Statement - II : If f(x) = sin x , then f(0) =f(2pi) .

Prove that the function f (x) = 5 is continuous at x = 2 .

If f(x-2)=2x^2+3x-5 , find f(x) and prove that f(-1) = 0.

If f(x)=x^2-2x+5 , then find f(1) .

If f(x)=|x^2-5x+6|, then f'(x) equals

a, b in RR be such that the function f given by f(x)=ln|x|+bx^(2)+ax,xne0 has extreme values at x=-1 and x = 2. Statement-I : f has local maximum at x = -1 and at x = 2. Statement-II : a=(1)/(2)" and "b=-(1)/(4) .

Let f: R->R be a continuous onto function satisfying f(x)+f(-x)=0AAx in R . If f(-3)=2 \ a n d \ f(5)=4 \ i n \ [-5,5], then the minimum number of roots of the equation f(x)=0 is

Let f: R->R be a continuous onto function satisfying f(x)+f(-x)=0AAx in R . If f(-3)=2 \ a n d \ f(5)=4 \ i n \ [-5,5], then the minimum number of roots of the equation f(x)=0 is