# How do you find the exact relative maximum and minimum of the polynomial function of #y=x^2 +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 #

Differentiating wrt

# dy/dx = 2x+1 #

For the derivative to vanish we have:

# dy/dx = 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]}