# calculus-derivatives

posted by .

Hello, please help me. I needed to find the derivative of f(x)= x^4 -2x^3 + x +1. I got f'(x)= 4x^3 -6x^2 +1. I would like to figure out the critical numbers so I can figure out where it increases and decreases, but I have no idea how to factor it... Is it even possible?

• calculus-derivatives -

tried x = ± 1 , no good
tried ± 1/2 and ahhh! x = 1/2 is a root
so (2x-1) is a factor
long division:
4x^3 -6x^2 +1 = (2x-1)((2x^2 - 2x-1)

2x^2 - 2x-1 = 0 gave me
x = (1 ± √3)/2

so there are 3 critical points to worry about.
take it from here.

• calculus-derivatives -

this factors into

2(2x-1)(x^2 - 2x - 1)
x = 1/2 or (1±√3)/2

Having that, you can find where f'<0 or f'>0

• calculus-derivatives -

Oooooh! Thank you two so much :) I'm more confident in regards to my test now, thank you

## Similar Questions

1. ### calculus

Hello. I need help finding the open intervals of this equation: f(x)=3x^2-12 I already took the derivative of it by using the derivative test and I got 2,-2 as critical numbers
2. ### calculus

Hello. I need help finding the open intervals of this equation: f(x)=3x^2-12 I already took the derivative of it by using the derivative test and I got 2,-2 as critical numbers

FOr the function f(x)=x^2e^x Find the critical points, increasing decreasing, first and second derivative and concavity I am having trouble finding the concavity >_< First derivative: xe^x(x+2) Second : e^x(x^2+4x+2) Critical …
4. ### Calculus

I finished this problem but I wanted some feedback because I don't know if it's entirely correct. Suppose that functions f and g and their derivatives with respect to x have the following values at x=2. f(x)=8 g(x)=2 f'(x)=1/3 g'(x)=-3 …
5. ### math

Okay. so say their is a list of numbers: x y 0 3 1 5 2 7 3 9 4 11 I know how to answer a question like "use an equation to figure out Y when X is..." but how do you figure do " figure out X when Y is" ?
6. ### Calculus - another question

"Find the absolute minimum value of the function f(x) = x ln(x)". I know that one of the critical values is 1 (domain restriction). Am I right?
7. ### CALCULUS

Consider the function: f(x) = x/(x^2 + 2) (a) Determine the intervals on which the function is concave up. Enter the leftmost interval first (e.g. (1,2) would come before (3,4)). (b) Determine the intervals on which the function is …
8. ### Calculus-derivatives

f(x) = (x-1)^(2/3)*(x+3) What are the critical numbers?
9. ### calculus-derivatives

Hello, please help me, I'm studying for a test. :) I won't say the question because I'd like to figure it out myself or try first, but I'm looking for a simpler way to go about this. I have to find the derivative of h(x)= (x)(x-1)^1/3 …
10. ### Calc BC

Figure out the 35th derivative for xsinx. You have to do a few derivatives by hand to figure our a pattern and then predict the 35th one

More Similar Questions