What is the minim point of the parabola y=x^2-2x-5?
The minim point of the parabola represents the extreme of the parabola. We'll have to verify if the function has a critical point. If so, then the function has a local extreme.
To determine the critical point, we'll have to calculate the 1st derivative of the function.
f'(x) = 2x - 2
Now, we'll cancel out f'(x):
f'(x) = 0 <=> 2x - 2 = 0 => x - 1 = 0 => x = 1
Since there is a critical point x = 1, then the function has a minimum point at f(1) = 1 - 2 - 5 = -6.
The coordinates of the minimum point of the parabola are: (1 , -6).