Final answer:
Without the specific definition of f(x) in the interval including x = 1, it is not possible to find f'(1). Generally, the derivative is calculated from the relevant formula and evaluated at x = 1.
Step-by-step explanation:
To find f'(1), or the derivative of the function f(x) at the point x = 1, we would need the specific definition of the function f(x). Since a piecewise function is described in the question, it's important to examine the formulas given for different intervals of x and compute the derivative based on the formula applicable to the interval that includes x = 1. However, the function definition for the relevant range is not provided in the information given. Therefore, it is not possible to find f'(1) without additional details about the function f(x) within the range including x = 1. Typically, to determine f'(1), you would take the derivative of the function that applies at x = 1 and simply substitute x with 1 in this derivative.
For problems involving probability functions (P(x)), one commonly finds the probability over an interval by computing the integral of the probability density function over that interval. However, the information provided about the functions is incomplete, so specific probabilities or areas under the curve cannot be calculated without the full context of the function definitions.