|BSM

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Understand the relationship between differentiability and continuity

Which one of the following function is continuous but not differentiable at the point x=3?

$f\left(x\right)=\left|x\right|$

$g\left(x\right)=\left|x-3\right|$

$h\left(x\right)=x^2$

Determine whether function $f\left(x\right)=\frac{4x^2-1}{2x-1}$ is ____________ at $x=\frac{1}{2}$ :

Continuous and differentiable

Continuous but non-differentiable

Differentiable but non-continuous

Neither continuous nor differentiable

Determine whether function $f\left(x\right)=6x^8$ is:

Continuous and differentiable

Continuous but non-differentiable

Differentiable but non-continuous

Neither continuous nor differentiable

If a function is differentiable at a point, it is necessarily continuous.

Yes

No

Is the sentence true or false?
A function is not differentiable if it is not continuous.

True

False

Determine whether function $g\left(x\right)=x^2$ is:

Continuous and differentiable

Continuous but non-differentiable

Differentiable but non-continuous

Neither continuous nor differentiable

Is the sentence true or false?
$f\left(x\right)=x+1$ f is a continuous and differentiable function at x=1.

True

False

Which one of the following functions is neither continuous nor differentiable on R?

$\left|x\right|$

$\left[x\right]$

$x^4$

Which one of the following function is continuous and differentiable at the point $x=1$ ?

$f\left(x\right)=\left|x\right|$

$g\left(x\right)=\left|x-1\right|$

$h\left(x\right)=x^2$

Is the sentence true or false?
Continuity of a function is the characteristic of a function by virtue of which, the graphical form of that function is a continuous wave.

True

False

Questions

Time

Score

Understand the relationship between differentiability and continuity

Which one of the following function is continuous but not differentiable at the point x=3?

﻿f(x)=∣x∣f\left(x\right)=\left|x\right|f(x)=∣x∣﻿

﻿g(x)=∣x−3∣g\left(x\right)=\left|x-3\right|g(x)=∣x−3∣﻿

﻿h(x)=x2h\left(x\right)=x^2h(x)=x2﻿

Determine whether function ﻿f(x)=4x2−12x−1f\left(x\right)=\frac{4x^2-1}{2x-1}f(x)=2x−14x2−1​﻿ is ____________ at ﻿x=12x=\frac{1}{2}x=21​﻿:

Continuous and differentiable

Continuous but non-differentiable

Differentiable but non-continuous

Neither continuous nor differentiable

Determine whether function ﻿f(x)=6x8f\left(x\right)=6x^8f(x)=6x8﻿ is:

Continuous and differentiable

Continuous but non-differentiable

Differentiable but non-continuous

Neither continuous nor differentiable

If a function is differentiable at a point, it is necessarily continuous.

Yes

No

Is the sentence true or false?A function is not differentiable if it is not continuous.

True

False

Determine whether function ﻿g(x)=x2g\left(x\right)=x^2g(x)=x2﻿ is:

Continuous and differentiable

Continuous but non-differentiable

Differentiable but non-continuous

Neither continuous nor differentiable

Is the sentence true or false?﻿f(x)=x+1f\left(x\right)=x+1f(x)=x+1﻿ f is a continuous and differentiable function at x=1.

True

False

Which one of the following functions is neither continuous nor differentiable on R?

﻿∣x∣\left|x\right|∣x∣﻿

﻿[x]\left[x\right][x]﻿

﻿x4x^4x4﻿

Which one of the following function is continuous and differentiable at the point ﻿x=1x=1x=1﻿?

﻿f(x)=∣x∣f\left(x\right)=\left|x\right|f(x)=∣x∣﻿

﻿g(x)=∣x−1∣g\left(x\right)=\left|x-1\right|g(x)=∣x−1∣﻿

﻿h(x)=x2h\left(x\right)=x^2h(x)=x2﻿

Is the sentence true or false?Continuity of a function is the characteristic of a function by virtue of which, the graphical form of that function is a continuous wave.

True

False

Incorrect

Great!

$f\left(x\right)=\left|x\right|$

$g\left(x\right)=\left|x-3\right|$

$h\left(x\right)=x^2$

Determine whether function $f\left(x\right)=\frac{4x^2-1}{2x-1}$ is ____________ at $x=\frac{1}{2}$ :

Determine whether function $f\left(x\right)=6x^8$ is:

Is the sentence true or false?
A function is not differentiable if it is not continuous.

Determine whether function $g\left(x\right)=x^2$ is:

Is the sentence true or false?
$f\left(x\right)=x+1$ f is a continuous and differentiable function at x=1.

$\left|x\right|$

$\left[x\right]$

$x^4$

Which one of the following function is continuous and differentiable at the point $x=1$ ?

$f\left(x\right)=\left|x\right|$

$g\left(x\right)=\left|x-1\right|$

$h\left(x\right)=x^2$

Is the sentence true or false?
Continuity of a function is the characteristic of a function by virtue of which, the graphical form of that function is a continuous wave.