Questions
The value of c In Lagrange’s theorem for the following for the function
a
π/4
b
π/2
c
2π/3
d
None of these
detailed solution
Correct option is B
f(5π6)=log sin(5π6)=log sinπ6 =log12=log2, f(π6)=logsinπ6=−log2. f'(c)=1sinxcosx=cotx By Lagrange’s mean value theorem,f(5π/6)−f(π/6)(5π/6)(π/6)=cotc ⇒cotc=0⇒c=π2 Thus, c=π2∈(π/6,5π/6).Talk to our academic expert!
Similar Questions
Consider the function on the interval the value of c satisfying the conclusion of Lagrange’s mean value theorem is ______________.
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