Question #c5468

1 Answer
Oct 17, 2017

Extreme (minimum) value of the function y is at x=(-1)/2

Explanation:

We have y=x^2+x+2

As we can see a>0 so its an upward facing parabola.
So it will have a minimum value.

The minumum value will be at x=(-b)/(2a)

Therefore, x=(-1)/2

                               OR

When we differentiate the function y we get

y^'=2x+1

When we find out the critical point of y^' it is

2x+1=0

2x=-1

x=(-1)/2

Therefore the function will be minimum at x=(-1)/2

When we put x=(-1)/2 in y we get

y=1/4-1/2+2

y=7/4

y=1.75

Also the graph for the function is

graph{x^2+x+2 [-6.024, 6.46, -0.516, 5.724]}

Here you can see the minimum value of the function y is at x=-0.5 which is y=1.75