# How do you find and classify all the critical points and then use the second derivative to check your results given #y=x^2+10x-11#?

##### 1 Answer

Vertex

Y-intercept

X-intercepts

#### Explanation:

Given -

#y=x^2+10x-11#

It is a quadratic equation .

It has only one critical point.

It is the vertex.

#x=(-b)/(2a)=(-10)/(2 xx 1)=-5#

At

#y= 25-50-11=25-61=-36#

Vertex is

Derivatives of the function are

#dy/dx=2x+10#

#(d^2y)/(dx^2)=2 > 0#

Its second derivative is greater than zero. The curve is concave upwards.

Its other important points are

Y-intercept

At

At

X- intercepts

At

# x^2+11x-x-11=0#

#x( x+11)-1(x+11)=0#

#(x+11)(x-1)=0#

#x+11=0#

#x=-11#

#x-1=0#

#x=1#

At points