Question

please show all work so i can understand

Write f(x)=ln((x^2 square root(x-4)/(x+1)^3)) in terms of lnx, ln(x+1), and ln(x-4). Then find f '(x).

Answer #1

please show steps by steps so i can understand
f (x) = (1/4)x^4-24x^2+1
(a) Find all the open intervals on which f increases/decreases,
and determine the relative extrema of f .
(b) Find all the open intervals on which f is concave up (down).
Then determine the x- coordinates of all inflection points of f .
Provide details with step by step to justify your answers!

please show steps by steps so i can understand
f (x) = (1/4)x^4-24x^2+1
(a) Find all the open intervals on which f increases/decreases,
and determine the relative extrema of f .
(b) Find all the open intervals on which f is concave up (down).
Then determine the x- coordinates of all inflection points of f .
Provide details with step by step to justify your answers!

Find derivatives (Please show work!)
1. f(x)=ln(5x^3)
2. f(x)=(ln^3)x
3. f(x)=e^(5x2+2)
4. f(x)=xe^2x
5. f(x)=xlnx

HW2:
Q1: find the multiplicity of the root
f(x)=((x-3)^2)*(ln(x-2))

The function f(x)=lnx has a Taylor series at a=4 . Find the
first 4 nonzero terms in the series, that is write down the Taylor
polynomial with 4 nonzero terms.

Solve the initial-value problem.
x2y' + 2xy = ln(x), y(1) =
7.
Please show all work neatly, line by line, and please justify
steps so that I can learn.
Thank you!

Find the linear approximation for f(x) = x^4+x-3 at x=0.98.
Please show all your work

1) Find f’(x), given f(x) = x^1/3 (lnx)
2)Find f(x), given f’’(x) = 3 , f’(0) =4 f(0) = -5
3) A ball is thrown upward with an initial velocity = 96 What is
the maximum height it reaches?
4) Find the area bounded by f(x) = x^2 +1 , g(x) = x +3

Newton's method: For a function ?(?)=ln?+?2−3f(x)=lnx+x2−3
a. Find the root of function ?(?)f(x) starting with
?0=1.0x0=1.0.
b. Compute the ratio |??−?|/|??−1−?|2|xn−r|/|xn−1−r|2, for
iterations 2, 3, 4 given ?=1.592142937058094r=1.592142937058094.
Show that this ratio's value approaches
|?″(?)/2?′(?)||f″(x)/2f′(x)| (i.e., the iteration converges
quadratically). In error computation, keep as many digits as you
can.

find critical numbers of
f(x)=2x^3 + x^2 - 2x
please show all work :)

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