Find the maximum value of 's' if 's' depends on 't' as s=-3t^2+15t+5
Answers
We have to find the maximum value of s if s depends on t as s = -3t² + 15t + 5
solution : here, s(t) = -3t² + 15t + 5
differentiating with respect to time, we get,
ds(t)/dt = -6t + 15
at ds(t)/dt = 0 = -6t + 15 ⇒t = 5/2
now again differentiating with respect to time,
d²s(t)/dt² = -6 < 0 at t = 5/2 [ well s"(t) is negative for all value of t but s'(t) = 0, give t = 5/2 so we consider t = 5/2]
hence maximum value of s will be at t = 5/2
now, maximum value of s = s(5/2) = -3(5/2)² + 15(5/2) + 5
= -3 × 6.25 + 37.5 + 5
= -18.75 + 42.5
= 23.75
Therefore the maximum value of -3t² + 15t + 5 is 23.75
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