Question

f(x) = |x - 2| + |x – 4| , show that f'(3) = 0​

Answer 1

Answer:

Hey mate here is your answer ...>.

Show that

f(x)=x1/3

f(x)=x1/3

is not differentiable at x=0x=0.

LHD at x=0

LHD at x=0

=limh→0f(0−h)−f(h)0−h−0

=limh→0f(0−h)−f(h)0−h−0

=limh→0−h1/3−h=limh→0−h−2/3

=limh→0−h1/3−h=limh→0−h−2/3

and similarly

RHD at x=0=limh→0h−2/3

RHD at x=0=limh→0h−2/3

If I directly substitute h=0h=0 both will be 00 or should I take 00 to the denominator. How do I solve this?

and I have another doubt:

How is

limx→0e−2/x=0

Assume f′(0)f′(0) exists. Consider g(x)=(f(x))3=xg(x)=(f(x))3=x.Then by the chain rule g′(0)=3(f(0))2f′(0)g′(0)=3(f(0))2f′(0). Since g′(0)=1g′(0)=1 and f(0)=0f(0)=0, we find 1=0⋅f′(0)1=0⋅f′(0), which is absurd.

For your second question (which you might prefereably have posted separately): We have

limx→0+e−2/x=0

limx→0+e−2/x=0

because −2/x→−∞−2/x→−∞, but

limx→0−e−2/x=+∞

limx→0−e−2/x=+∞

because now −2/x→+∞−2/x→+∞. So limx→0e−2/xlimx→0e−2/x does not exist.

hope it's helpful for you....

thanks

Answer 2

Show that

thatf(x)=x1/3

thatf(x)=x1/3f(x)=x1/3

thatf(x)=x1/3f(x)=x1/3is not differentiable at x=0x=0.

thatf(x)=x1/3f(x)=x1/3is not differentiable at x=0x=0.LHD at x=0

thatf(x)=x1/3f(x)=x1/3is not differentiable at x=0x=0.LHD at x=0LHD at x=0

thatf(x)=x1/3f(x)=x1/3is not differentiable at x=0x=0.LHD at x=0LHD at x=0=limh→0f(0−h)−f(h)0−h−0

thatf(x)=x1/3f(x)=x1/3is not differentiable at x=0x=0.LHD at x=0LHD at x=0=limh→0f(0−h)−f(h)0−h−0=limh→0f(0−h)−f(h)0−h−0

thatf(x)=x1/3f(x)=x1/3is not differentiable at x=0x=0.LHD at x=0LHD at x=0=limh→0f(0−h)−f(h)0−h−0=limh→0f(0−h)−f(h)0−h−0=limh→0−h1/3−h=limh→0−h−2/3

thatf(x)=x1/3f(x)=x1/3is not differentiable at x=0x=0.LHD at x=0LHD at x=0=limh→0f(0−h)−f(h)0−h−0=limh→0f(0−h)−f(h)0−h−0=limh→0−h1/3−h=limh→0−h−2/3=limh→0−h1/3−h=limh→0−h−2/3

thatf(x)=x1/3f(x)=x1/3is not differentiable at x=0x=0.LHD at x=0LHD at x=0=limh→0f(0−h)−f(h)0−h−0=limh→0f(0−h)−f(h)0−h−0=limh→0−h1/3−h=limh→0−h−2/3=limh→0−h1/3−h=limh→0−h−2/3and similarly

thatf(x)=x1/3f(x)=x1/3is not differentiable at x=0x=0.LHD at x=0LHD at x=0=limh→0f(0−h)−f(h)0−h−0=limh→0f(0−h)−f(h)0−h−0=limh→0−h1/3−h=limh→0−h−2/3=limh→0−h1/3−h=limh→0−h−2/3