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LoginLet a function f(x) defined on [3,6] be given by `f(x)={{:(,log_(e)[x],3 le x lt5),(,|log_(e)x|,5 le x lt 6):}` then f(x) is
A. continuous and differentiable on [3,6]
B. continuous on [3,6] but not differentiable at x=4,5
C. differentiable on [3,6] but not continuous at x=4,5
D. none of these
General Awareness CONTINUITY-AND-DIFFERENTIABILITY IN GENERAL AWARENESS . 2 years ago
+10 pts
We have
`f(x)={{:(,log_(e)3,3 le x lt 4),(,log_(e)4,4 le x lt 5),(,log_(e)x,5 le x lt 6):}`
Clearly, f(x) is continuous and differentiable `[3,4) uu (4,5) uu (5,6)`
At x=4, we have
`underset(x to 4^(-))lim f(x)=log_(e) 3 and underset(x to 4^(+))lim f(x)=log_(e)4`
`therefore underset(x to 4^(-))lim f(x)ne underset(x to 4^(+))lim f(x)`
Thus, f(x) is neither continuous nor differentiable at x=4, At x=5, we have
So, f(x) is neither continuous nor differentiable at x=5.
Posted on 06 Oct 2022, this text provides information on General Awareness related to CONTINUITY-AND-DIFFERENTIABILITY IN GENERAL AWARENESS. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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