differentiation, relative extrema, inflection points, etc

[abby_07]

i need help finding all relative extreme and points of inflection
i dont know if i am doing it correctly

1) Find all relative extrema and points of inflection for f(x) = x - sin(x) on the interval 0 < x < 4pi

f'(x)=1-cosx=0
f'(x)=-cos=-1
critical #2 pi
f"(x)=sinx
f"(2pi)=0
relative min. (0,0)
f"(x)=sinx=0
f"(x)=pi
point of inflection is (pi,0)

then i have no idea how to do this problem

2) Find values of a, b, c, and d such that the cubic polynomial function f(x) = ax^3 + bx^2 + cx + d satisfies the indicated conditions:

. . .relative maximum at (2, 4)
. . .relative minimum at (4, 2)
. . .inflection point at (3,3)

can you please help
thank you

 

[stapel]

1) What happened to the variable? You somehow ended up with "cos() = 1"...? What is the meaning of "critical#2"...? Was there a first critical number that I overlooked...?

2) If there are relative extrema at x = 2 and x = 4, what can you say about the value of the derivative at these points? If there is an inflection point at x = 3, what can you say about the value of the second derivative at this point? Use this information to create three equations. Then use any of the three data points to form a fourth equation. This will give you four equations in four unknowns. Solve the system.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.