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For the function f(x)=(x^(100))/(100)+(...

For the function
`f(x)=(x^(100))/(100)+(x^(99))/(99)+...+(x^2)/2+x+1`
. Prove that `f^(prime)(1)=100f^(prime)(0)`.

Text Solution

AI Generated Solution

To prove that \( f'(1) = 100 f'(0) \) for the function \[ f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + \cdots + \frac{x^2}{2} + x + 1, \] we will first find the derivative \( f'(x) \) and then evaluate it at \( x = 1 \) and \( x = 0 \). ...
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