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Question
if `f(x) = (x - 4)/(2sqrt(x))`, then f'(1) is ______.
Options
`5/4`
`4/5`
1
0
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Solution
if `f(x) = (x - 4)/(2sqrt(x))`, then f'(1) is `5/4`.
Explanation:
Given that `f(x) = (x - 4)/(2sqrt(x))`
∴ f'(x) = `1/2[(sqrt(x) * 1 - (x - 4) * 1/(2sqrt(x)))/x]`
= `1/2 [(2x - x + 4)/(2sqrt(x) * 4)]`
= `1/2[(x + 4)/(2(x)^(3/2))]`
∴ f'(x) at x = 1
= `1/2 [(1 + 4)/(2 xx 1)]`
= `5/4`
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