Consider the following function f(x) = 1 / x^23; find f(1) and f'(1)

To find f(1), we simply substitute x = 1 into the function:

f(1) = 1 / (1)^23 = 1

Now, to find f'(x), we need to differentiate the function f(x). The function can be rewritten as:

f(x) = x-23

Using the power rule of differentiation, which states that d/dx[x^n] = n*x^(n-1), we can differentiate:

f'(x) = -23 * x-24

Now, we find f'(1) by substituting x = 1 into the derivative:

f'(1) = -23 * (1)-24 = -23

In summary:

  • f(1) = 1
  • f'(1) = -23

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