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):
f'(x)=( x^2+x-2)'=(x^2)'+(x)'-(2)'
f'(x)=2x+1
Now we
have to calculate the equation of the first
derivative:
2x+1=0
2x=-1
x=-1/2
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).
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