Let us find the value of the input variable at which the maximum of function V=f(t)=IRsinωt occurs. It follows that f′(t)=ωIRcosωt=0 implies ωt=2π+πn, and thus t=2ωπ+ωπn. Since
f′′(t)=−ω2IRsinωt and f′′(2ωπ+ωπn)=−ω2IRsinω(2ωπ+ωπn)=−ω2IRsin(2π+πn),
we conclude that f′′(2ωπ+ω2πk)==−ω2IRsin(2π+2πk)=−ω2IRsin(2π)=−ω2IR<0
and f′′(2ωπ+ωπ(2k+1))==−ω2IRsin(2π+π(2k+1))=ω2IRsin(2π)=ω2IR>0. Therefore, the points tk=2ωπ+ω2πk, where k∈N, is the values of the input variable at which the maximum of function V=f(t)=IRsinωt occurs.
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