If f(x)=|1−4x2|,0≤x<1[x2−2x],1≤x<2, where [.] denotes the greatest integer function, then f(x) is

f(x)={1−4x24x2−1−1 0≤x≤1212≤x≤11≤x≤2 f(12−)=f(12+)=f(12)& f(1)≠f(1−) ⇒ fis not continuous at x=1∴ f is non differentiable at x=1

If f(x)=|1−4x2|,0≤x<1[x2−2x],1≤x<2, where [.] denotes the greatest integer function, then f(x) is

f(x)={1−4x24x2−1−1 0≤x≤1212≤x≤11≤x≤2 f(12−)=f(12+)=f(12)& f(1)≠f(1−) ⇒ fis not continuous at x=1∴ f is non differentiable at x=1

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If $f (x) = \{\begin{cases} | 1 - 4 x^{2} |, & 0 \leq x < 1 \\ [x^{2} - 2 x], & 1 \leq x < 2 \end{cases}$ , where $[.]$ denotes the greatest integer function, then $f (x)$ is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

differentiable for all x

non-differentiable at $x = 1$

continuous at $x = 1$

Discontinuous at $x = \frac{1}{2}$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$f (x) = {\begin{matrix} 1 - 4 x^{2} \\ 4 x^{2} - 1 \\ - 1 \end{matrix} \begin{matrix} 0 \leq x \leq \frac{1}{2} \\ \frac{1}{2} \leq x \leq 1 \\ 1 \leq x \leq 2 \end{matrix}$
$f ({\frac{1}{2}}^{-}) = f ({\frac{1}{2}}^{+}) = f (\frac{1}{2})$
& $f (1) \neq f (1^{-}) \Rightarrow$ fis not continuous at $x = 1$
$∴ f$ is non differentiable at $x = 1$