Discover the minimum value of the function x^2+x-2.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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