Final answer:
To find the critical point of the function f(x) = (-x + 4)5 + 1, calculate the derivative and set it equal to zero. The only critical point is x = 0, which is a minimum.
Step-by-step explanation:
The given function is f(x) = (-x + 4)5 + 1. To find the critical point, we need to calculate the derivative of the function and set it equal to zero.
f'(x) = 5(-1)x^4 + 0 = 0
From this equation, we can see that the only critical point is x = 0. To determine if it is a maximum, minimum, or point of inflection, we need to find the second derivative.
f''(x) = 20x^3
Since the second derivative f''(x) is positive for all values of x, the critical point x = 0 is a minimum.