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