Question

What is the value of x where x^2 - x + 3 is a minimum?

Answer 1

Answer:

We know that to find the maximum or minimum value of a function, we calculate the first derivative of the function and then equate it to zero for finding the critical points(the points where the equation attains its maximum,minimum value or inflection) and then again differnetiate function and substitute the critical points into the second derivative if the value come out to be positive the critical points give minimum if the value of 2nd derivative come out to be negative it gives maximum value…

Using the same concept here, we get

The first derivative comes to be

dy/dx=2x−1

equating it to zero the critical point comes we get

x=1/2

now differentiating it again, we get,

d²y/dx²=2

which is a positive value hence the function attains minimum value at x=1/2

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