Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability
A function f(x) is defined in the interval [1,4] as follows f(x)= array ll _e|x|, & 1 x 3 | _e x |, & 3 x 4 array . then the graph of f(x)
Options
- Ais broken at two points
- Bis broken at exactly one point
- Cdoes not have a definite tangent at two points
- Ddoes not have a definite tangent at more than two points
Correct answer
C. does not have a definite tangent at two points
Step-by-step solution
f(x) array cc 0, & 1 x 2 _e 2, & 2 x 3 _e x, & 3 x 4 array . clearly f(x) is continuous and differentiable everywhere except possibly at x=2,3 As _ x 2⁻ f(x)=0, _ x 2⁺ f(x)= _e 2f(x) is not continuous at x=2 _ x 3⁺ f(x)= _e 2, _ x 3⁺ f(x)= _e 3 f(x) is not continuous at x=3 Hence f(x) is not derivable at x=2,3 .