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Question
If `f(x) = 1 + x + x^2/2 + ... + x^100/100`, then f'(1) is equal to ______.
Options
`1/100`
100
does not exist
0
Solution
If `f(x) = 1 + x + x^2/2 + ... + x^100/100`, then f'(1) is equal to 100.
Explanation:
Given `f(x) = 1 + x + x^2/2 + ... + x^100/100`
`f"'"(x) = 1 + (2x)/2 + ... + (100x^99)/100`
∴ `f""(1)` = 1 + 1 + ... + 1 (100 times) = 100
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