I will do part of one but really think you should try it yourself first and then ask for help with specific questions.
In general look for what it says to look for.
For example the second one
g(x) = x^3 - 6 x^2 + 9x
first of all what happens to this for large negative x and for large positive x?
for large x magnitude it will look like x^3 so it will go off to negative infinity for large negative x and off to positive infinity for large positive x, sloping ever more steeply (concave)
Now where will it be zero?
set it equal to zero
x^3 - 6 x^2 + 9x = 0 = x(x^2-6x+9)=x(x-3)(x-3)
so zero if x = 0 and double zero (just touches the x axis, does not go through) at x = 3
Now we have a pretty good idea what it looks like already.
It snakes up from -oo on the left, goes through (0,0) headed up to the right, then dips down to the x axis, just touching, before heading up to the right.
Now where is it horizontal between x = 0 and x = 3 ?
take derivative and set to zero
dg/dx = 3 x^2 -12 x + 9
set to zero and factor out 3
0 = x^2 -4x + 3
0 = (x-1)(x-3)
so horizontal at x = 1 (and as we knew at x=3)
What is g at that extreme at x = 1?
g = 1^3 - 6*1^2 + 9*1
=1 - 6 + 9
That should about do it, you can sketch it pretty neatly
calculus - Jena. Stop it, or you will be banned. Using the chain rule, how do i ...
physical science - How to learn to do the formulas for finding speed, distnace, ...
CALCULUS - what is the derivative of ln(x-1)? If you are studying the calculus ...
Math (pre-calculus) - Hey! I have a domain and range question! I don't remember ...
hey got a question here - hey if dy/dx= -2 why is it wrong to say that y is ...
calculus - Hey I am working on differentiation/quotient rule for this problem...
urgent urgent urgent - what is the chemical make up of actin and myocin
HEY DRWLS!! I have a question - You're a genius, so can you please help me with ...
urgent urgent algebra - find the composite function fog f(X) = 1/X-5,g(x)-6/x ...
urgent alg 1 - add or subtract 2 2 (2t -8t)+ (8t + 9t) second question 3 2 3 (t...