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JAMB Mathematics 2019 Paper

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Question : 36

Total: 73

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

50 units per sec
35 units per sec
22 units per sec
13 units per sec

Solution:

Concept:

Differentiation of a product of two functions using the product rule.

Explanation:

Given

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

.

Let

u = 4t + 3

and

v = t - 2

.

Then

\frac{du}{dt} = 4

and

\frac{dv}{dt} = 1

.

Using the product rule:

\frac{ds}{dt} = u\frac{dv}{dt} + v\frac{du}{dt}

.

So,

\frac{ds}{dt} = (4t + 3)(1) + (t - 2)(4)

.

Simplify:

\frac{ds}{dt} = 4t + 3 + 4t - 8 = 8t - 5

.

When

t = 5

secs:

\frac{ds}{dt} = 8(5) - 5

.

Thus,

\frac{ds}{dt} = 40 - 5 = 35

.

The rate of change is

35

units per sec.

Answer:

B. 35 units per sec

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