How do you find the exact relative maximum and minimum of the polynomial function of y=x^2 +x -1y=x2+x−1?
1 Answer
Jun 26, 2017
we have a minimum at
Explanation:
To find a min/max we look for values of
We are dealing with a positive quadratic so we expect a single minimum.
We have:
y = x^2 + x -1 y=x2+x−1
Differentiating wrt
dy/dx = 2x+1 dydx=2x+1
For the derivative to vanish we have:
dy/dx = 0 => 2x+1 =0 dydx=0⇒2x+1=0
:. x=-1/2
Differentiating again wrt
(d^2y)/(dx)^2 = 2
So when
Finally, When
Thus we have a minimum at
graph{y = x^2 + x -1 [-10, 10, -5, 5]}