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Algebra of Derivatives

Write the neg...

Question

Write the negation of "some continuous functions are differentiable".

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Solution

Negation of "some continuous functions are differentiable" is "All non continuous functions are not differentiable ".

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Q. Write the converse, inverse and contrapositive of the following statements : "If a function is differentiable then it is continuous".

Q. The function

f (x) = \frac{\sin (π [x - π])}{4 + {[x]}^{2}}

, where [⋅] denotes the greatest integer function, is
(a) continuous as well as differentiable for all x ∈ R
(b) continuous for all x but not differentiable at some x
(c) differentiable for all x but not continuous at some x.
(d) none of these

Q. Write an example of a function which is everywhere continuous but fails to differentiable exactly at five points.

Q. The negative of the statement “All continuous functions are differentiable.”

Q. Say true or false.

Every continuous function is always differentiable.

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