So, f(x) is
Q. 20 Examine the differentiability of f, where f is defined by
x[x]
if O S x<2.
f(x) =
at x = 2.
(x - 1)x, if 2 < x < 3
/
Answers
Answered by
1
Step-by-step explanation:
f(1
−
)=
h→0
lim
(1−h)0=0
f(1
+
)=
h→0
lim
1+h=1
Since f is not continuous at x=1, its also not differentiable at that point.
f(2
−
)=
h→0
lim
(2−h)(1)=2
f(2
+
)=
h→0
lim
(2+h−1)2=2
f
′
(2
−
)=
h→0
lim
−h
2−h−2
=1
f(2
+
)=
h→0
lim
h
2+2h−2
=2
Hence, the function is continuous but not differentiable at x=2.
Answered by
1
Step-by-step explanation:
f(1
−
)=
h→0
lim
(1−h)0=0
f(1
+
)=
h→0
lim
1+h=1
Since f is not continuous at x=1, its also not differentiable at that point.
f(2
−
)=
h→0
lim
(2−h)(1)=2
f(2
+
)=
h→0
lim
(2+h−1)2=2
f
′
(2
−
)=
h→0
lim
−h
2−h−2
=1
f(2
+
)=
h→0
lim
h
2+2h−2
=2
Hence, the function is continuous but not differentiable at x=2.
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