Discover the minimum value of the function x^2+x-2.
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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
=> -9/4
=> -2.25
The minimum value of the function is -2.25
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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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