If S = (4t + 3)(t – 2), find ds/dt when t = 5 secs.

Explanation

\(s = (4t + 3)(t - 2)\)

\(\frac{\mathrm d s}{\mathrm d t} = (4t + 3)(1) + (t - 2)(4)\)

= \(4t + 3 + 4t - 8\)

= 8t - 5

\(\frac{\mathrm d s}{\mathrm d t} (t = 5 secs) = 8(5) - 5\)

= 40 - 5 

= 35 units per sec

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