Number of points where fx-x-sin2- x is not differentiable if x-7-10 is where - denotes the greatest integer function

F(x)=[x]sin^2(π x) f(x)= 7sin^2(π x), amp;x ∈( 7, 6) 0, amp; x= 6 6sin^2(π x), amp;x∈( 6, 5) 0, amp;x= 5 … amp;… … nbsp; amp;… … nbsp; ...

128

You visited us 128 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Right Hand Derivative

Number of poi...

Question

Number of points where $f (x) = [x] {sin}^{2} (π x)$ is not differentiable if $x \in (- 7, 10)$ is (where $[.]$ denotes the greatest integer function)

15

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

17

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $0$
$f (x) = [x] {sin}^{2} (π x)$
$f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - 7 {sin}^{2} (π x), & x \in (- 7, - 6) 0, & x = - 6 - 6 {sin}^{2} (π x), & x \in (- 6, - 5) 0, & x = - 5 \dots & \dots \dots & \dots \dots & \dots 0, & x = 9 9 {sin}^{2} (π x), & x \in (9, 10) \end{matrix}$
Clearly $f (x)$ is continuous for $x \in (- 7, 10)$

$f^{'} (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - 7 sin (2 π x), & x \in (- 7, - 6) 0, & x = - 6 - 6 sin (2 π x), & x \in (- 6, - 5) 0, & x = - 5 \dots & \dots \dots & \dots \dots & \dots 0, & x = 9 9 sin (2 π x), & x \in (9, 10) \end{matrix}$
Clearly $f (x)$ is differentiable for $x \in (- 7, 10)$
Hence, there is no such point where $f (x)$ is not differentiable for $x \in (- 7, 10)$

Suggest Corrections

Similar questions

Q. The points where the function

f (x) = [x] + | 1 - x |, - 1 \leq x \leq 3

, where

[.]

denotes the greatest integer function, is not differentiable are

Q. The set of points where the function

f (x) = [x] + | 1 - x |, - 1 \leq x \leq 3

, where

[.]

denotes the greatest integer function, is not differentiable, is

If f(x) = [sin x] + [cos x], $x \in [0, 2 π]$ , where [.] denotes the greatest integer function. Then, the total number of points, where f(x) is non – differentiable, is

Q. Let

f (x) = [n + p sin x], x \in (0, π), n \in Z

and

p

is prime number, where

[.]

denotes the greatest integer function. Then, the number of points where

f (x)

is not differentiable, are

Q. The number of points where

f (x) = [sin x + cos x]

(where []denotes greatest integer function),

x

ϵ (0, 2 π)

is not continuous is :

Join BYJU'S Learning Program

Number of points where f(x)=[x]sin2(πx) is not differentiable if x∈(−7,10) is (where [.] denotes the greatest integer function)

Number of points where $f (x) = [x] {sin}^{2} (π x)$ is not differentiable if $x \in (- 7, 10)$ is (where $[.]$ denotes the greatest integer function)