Discover the minimum value of the function x^2+x-2.
To find the minimum value of x^2+x-2 we find the derivative and equate it to 0 to solve for x. Using the value of x in the function we can find the lowest value.
f(x) = x^2 + x - 2
f'(x) = 2x + 1
2x + 1 = 0
=> x = -1/2
f(-1/2) = x^2 + x - 2
=> (-1/2)^2 +(-1/2) - 2
=> 1/4 - 1/2 - 2
The minimum value of the function is -2.25
To establish the minimum value of a function, we'll have to calculate the first derivative of the function.
Let's find the first derivative of the function f(x):
Now we have to calculate the equation of the first derivative:
That means that the function has an extreme point, for the critical value x=-1/2.
f(-1/2) = 1/4 - 1/2 - 2
f(-1/2) = (1-2-8)/4
f(-1/2) = -9/4
The minimum point of the function is (-1/2 ; -9/4).