The number of point(s) of non-differentiability for $f (x) = [e^{x}] + | x^{2} - 3 x + 2 | in (- 1, 3)$ is ( where [.] denotes greatest integer function, $e^{3} = 20.1$ )

Open in App

Solution

Given : $f (x) = [e^{x}] + | x^{2} - 3 x + 2 | & x \in (- 1, 3)$
$∵ e^{x}$ is increasing function $\Rightarrow e^{x} \in (\frac{1}{e}, e^{3})$ for $x \in (- 1, 3)$
$\Rightarrow e^{x} \in (0.36, 20.1)$
$\Rightarrow [e^{x}]$ is not differentiable at $20$ integral points.
and $| x^{2} - 3 x + 2 | = | (x - 2) (x - 1) |$ is non differentiale at $x = 1, 2$
Clearly, $e^{x}$ is not integer at $x = 1, 2$
$∴$ Total $22$ points of non-differentiability.

Suggest Corrections

Similar questions

f (x) = \infty \prod k = 1 ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ \frac{1 + 2 cos (\frac{2 x}{3^{k}})}{3} ⎞ ⎟ ⎟ ⎟ ⎟ ⎠

, then the number of points where

[x f (x)] + | x f (x) | + (x - 1) | x^{2} - 3 x + 2 |

is non-differentiable in

x \in (0, 3 π)

is equal to (where [.] denotes the greatest integer function)

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. 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)

Q. The function f (x) = x − [x], where [⋅] denotes the greatest integer function is
(a) continuous everywhere
(b) continuous at integer points only
(c) continuous at non-integer points only
(d) differentiable everywhere

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

Join BYJU'S Learning Program

The number of point(s) of non-differentiability for f(x)=[ex]+|x2−3x+2| in (−1,3) is ( where [.] denotes greatest integer function, e3=20.1 )

The number of point(s) of non-differentiability for $f (x) = [e^{x}] + | x^{2} - 3 x + 2 | in (- 1, 3)$ is ( where [.] denotes greatest integer function, $e^{3} = 20.1$ )