$$f(x) = x^3 + 4x^2 - x - 4$$

What are the steps you would follow to graph f(x)? Describe the end behavior of the graph of f(x).

Question

$$f(x) = x^3 + 4x^2 - x - 4$$

What are the steps you would follow to graph f(x)? Describe the end behavior of the graph of f(x).

camerondoherty · Answer

@surjithayer 
Do you know anything about this?
Im stumped. :/

anonymous · Answer

$$f \left( x \right)=x^3+4x^2-x-4=x^2\left( x+4 \right)-1\left( x+4 \right)=\left( x+4 \right)\left( x^2-1 \right)$$
$$=\left( x+4 \right)\left( x+1 \right)\left( x-1 \right)$$
when x=0,f(x)=-4
f(x)=0, when x=-4,-1,1
$$f \prime \left( x \right)=3x^2+8x-1,$$
put f'(x)=0,find x and then f(x) at these points
at these points tangent is parallel to x axis
f(x) is increasing if f'(x)>0 and find the interval for x.
f(x) is decreasing if f'(x)<0 and find the interval for x.
keeping these points in mind you can draw the graph considering f(x)=y

camerondoherty · Answer

Just to clear something up
So using this equation
$$f \prime \left( x \right)=3x^2+8x-1,$$You sub the values for x, and find f(x)?
Then you draw the graph accordingly? c:

camerondoherty · Answer

Sorry that took so long to type
I had it there, but the page kept going off somehow and I wasn't able to post it

anonymous · Answer

some times it is difficult to understand if it is increasing or decreasing

camerondoherty · Answer

Wait, but you do find f(x) and if it is greater than 0 it is increasing?

anonymous · Answer

no, I have written $$f \prime \left( x \right)>0$$
if it is increasing.

camerondoherty · Answer

Oh I see, Thank You so much c:

anonymous · Answer

yw