Given the parabola g(x) = 5x^2 - 5x + 7.
We need to find the minimum value.
First, we need to find the first derivative.
==> g'(x) = 10x - 5
Now we will calculate the critical values which is the derivative zeros:
==> 10x - 5 = 0
==>...
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Given the parabola g(x) = 5x^2 - 5x + 7.
We need to find the minimum value.
First, we need to find the first derivative.
==> g'(x) = 10x - 5
Now we will calculate the critical values which is the derivative zeros:
==> 10x - 5 = 0
==> 10x = 5
==> x = 1/2.
Since the sign of x^2 is positive, then we know that the function has a minimum value at x= 1/2
Then the function has a minimum value at x= 1/2
==> g(1/2) = 5(1/2)^2 - 5(1/2) + 7
= 5/4 - 5/2 + 7
= ( 5 - 10 + 28)/4
= 23/4
Then, the minimum values is: f(1/2) = 23/4