Question

If a derivative of a function is continous at a point then:
1. Derivative of a function does not exist
2. Function is differentiable at that point
3. Function is not continuous at that point
4. Function is not differentiable at that point​

Answer 1

$\huge{\color{white}{\fcolorbox {magenta}{navy}{ANWSER}}}$

Left-hand derivative of f(x)=Lf′(x)

=limh→0−f(1+h)−f(1)h

=limh→0+f(1−h)−f(1)−h

=limh→0+(1−h)2+2−3−h

=limh→0+h2−2h−h

=limh→0+(2−h)=2

AND

Right-hand derivative of f(x)=Rf′(x)

=limh→0+f(1+h)−f(1)h

=limh→0+(1+h)+2−3h

=limh→0+h+3−3h

=limh→0+1=1

Since Lf′(x)≠Rf′(x), so the function f(x) is not differentiable at x=1.

Answer 2

Step-by-step explanation:

4. Function is not differentiable at that pointssh

${6 { {?}^{2x5} }^{2} {5}^{2} } { {? {}^{2} }^{2} ?}^ud1573 - y255)5221 |1332|$