Consider the function: f(x) =3/4x^4 - x^3 -3x^2 + 6x

Determine the interval(s) where f(x) is increasing (if any) and the interval(s) where f(x) is decreasing (if any).

Question

Consider the function: f(x) =3/4x^4 - x^3 -3x^2 + 6x

Determine the interval(s) where f(x) is increasing (if any) and the interval(s) where f(x) is decreasing (if any).

nathanjhw · Answer

@nincompoop

myininaya · Answer

$$f(x)=\frac{3}{4}x^4-x^3-3x^2+6x \ \text{ First step is to differentiate }$$

myininaya · Answer

Then find when f'=0

myininaya · Answer

Then we will draw a number line and test intervals.

myininaya · Answer

Can you find f'?

nathanjhw · Answer

f' = 3x^3 -3x^2 -6x +6

myininaya · Answer

ok and then we need to find when f'=0

myininaya · Answer

it looks like you can factor by grouping if i'm not mistaken

nathanjhw · Answer

3(x-1)(x^2-2)

myininaya · Answer

$$f'(x)=3x^2(x-1)-6(x-1) \ f'(x)=(x-1)(3x^2-6)$$
now set both factors equal to zero and solve to find when f'=0

myininaya · Answer

yes that factorization works awesome too

myininaya · Answer

I left my 3's 
either way

nathanjhw · Answer

x = 1 and x =+- sqrt2

myininaya · Answer

|dw:1421968754166:dw|
we have 4 intervals to check