Which of the followings are true?
A. Let , then is differentiable in
B. For all positive numbers , function that is defined over all reals is differentiable in
C. If polynomials and satisfy and at least one of and is an identity function.
This problem is a part of <True or False?> series .
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
A.
f ′ ( x ) = 2 x and f ( x ) − f ′ ( x ) = x 2 − 2 x + 1 = ∣ x − 1 ∣ .
Therefore the expression is not differentiable at x = 1 .
∴ FALSE
B.
(counterexample)
f ( x ) = x 3 1 is not differentiable at x = 0 , because f ′ ( x ) = 3 x 3 2 1 .
∴ FALSE
C.
(counterexample)
If f ( x ) = 2 x and g ( x ) = 3 x , f ( g ( x ) ) = 6 x = g ( f ( x ) ) , but neither f nor g is an identity function.
∴ FALSE
Therefore, none of them are true.