5. For the function ?(?)=−3?^4
−12?^3
Find the domain and intercepts.
Find the critical numbers, intervals where f (x) is increasing
and decreasing, and any local maximum and local minimum points
(find both coordinates).
Find the intervals where f (x) is concave up and concave down
and any inflection points (find both coordinates).
Use this information to sketch the graph of f (x).
Consider the function ?(?)=(?^(4/5))*(?−3). This function has
two critical numbers ?<?
1) Then ?= ? and ? = ?.
2) For each of the following intervals, tell whether ?(?) is
increasing or decreasing.
(−∞,?]: ?
[?,?]: ?
[?,∞): ?
3) The critical number A is ? and the critical number B is ? (a
relative maximum / a relative minimum / neither max nor min )
There are two numbers ?<? where either ?″(?)=0 or f″(x) is
undefined.
4) Then C...
1.
Find the critical numbers of the function f (x) = x^3− 12x in the
interval [0, 3]. Then find the absolute maximum and the absolute
minimum of f(x) on the interval [0,3].
2. Using only the limit definition of derivative, find the
derivative of f(x) = x^2− 6x (do not use the formulas of
derivatives).
Let G = Z4 × Z4, H = ⟨([2]4, [3]4)⟩.
(a) Find a,b,c,d∈G so that G is the disjoint union of the 4
cosets a+H,b+
H, c + H, d + H. List the elements of each coset.
(b) Is G/H cyclic?
g(x, y) = 2x 3 + 9xy2 + 15x 2 +
27y2
Find all the critical points of the following functions. For
each critical point of g(x, y), determine whether g has a local
maximum, local minimum, or saddle point at that point.
1) Find y as a function of t if 9y′′+24y′+32y=0,
y(0)=5,y′(0)=8. y(t)=
2) Find y as a function of x if y′′′+16y′=0,
y(0)=−5, y′(0)=−32, y′′(0)=−32. y(x)=
3) Find y as a function of t if 9y′′−12y′+40y=0,
y(1)=5,y′(1)=9. y=
How do I graph this step function?
f(t) = -3(2t-3)H(t-2) + (2t-1)H(t-1)
Please show step by step.
How is it the same graph as
f(t) = H(t-1)-3H(t-2)+H(t-1)*2(t-1)-H(t-2)*6(t-2)?
Please show why as well.