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Question
A table of values of f, g, f' and g' is given:
| x | f(x) | g(x) | f'(x) | g'(x) |
| 2 | 1 | 6 | –3 | 4 |
| 4 | 3 | 4 | 5 | –6 |
| 6 | 5 | 2 | –4 | 7 |
If s(x) = f[9 − f (x)] find s'(4).
Solution
s(x) = f[9 − f(x)]
∴ s'(x) = `d/dx`{f[9 − f(x)]}
= f'[9 − f(x)].`d/dx`[9 − f(x)]
= f'[9 − f(x)].[0 − f'(x)]
= − f'[9 − f(x)].f'(x)
∴ s'(4) = − f'[9 − f(4)].f'(4)
= − f'[9 − 3].f'(4) ...[∵ f(x) = 3, when x = 4]
= − f'(6).f'(4)
= − (− 4)(5) ...[From the table]
= 20.
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