Question

Mr. Optimal wants to find the values of x ? [0, 2?] that minimize the functions f(x) = sin(x), g(x) = 5 sin(x), and h(x) = sin(5x) using Generalized Pattern Search. Please sort the functions (i.e., f, g, and h) based on the difficulty of finding the desired value using Generalized Pattern Search, and please explain your answer.

Answer #1

Consider the functions f(x) and g(x), for which f(0)=2, g(0)=4,
f′(0)=12 and g′(0)= -2
find h'(0) for the function h(x) = f(x)/g(x)

1a.) Find the linearization of the function f(x) = (sin x+1)^2
at a = 0.
1b.) Differentiate the two functions below.
f(x) = ln(e^x - sin x) ; g(x) = e^-x^2

suppose and are functions that are differentiable at x=0 and
that f(1)=2, f'(1)=-1, g(1)=-2, and g'(1)=3. Find the value of
h'(1).
1) h(x)=f(x) g(x)
2) h(x)=xf(x) / x+g(x)

The table below shows values for four differentiable functions.
Suppose we know the following things:
h'(x) = g(x)
g'(x) = f(x)
f'(x) = b(x)
b'(x) = h(x)
0
1
2
3
4
b(x)
2
4
3
1
0
f(x)
1
4
2
3
0
h(x)
2
0
3
1
4
g(x)
2
0
4
3
1
a) What is intergal from a = 2 and b = 4 f(x) dx?
b) What is intergal from a = 0 and b =...

Q 1) Consider the following functions.
f(x) = 2/x, g(x) = 3x + 12
Find (f ∘ g)(x).
Find the domain of (f ∘ g)(x). (Enter your answer using interval
notation.)
Find (g ∘ f)(x).
Find the domain of (g ∘ f)(x). (Enter your answer using
interval notation.)
Find (f ∘ f)(x).
Find the domain of (f ∘ f)(x). (Enter your answer using
interval notation.)
Find (g ∘ g)(x).
Find the domain of (g ∘ g)(x). (Enter your answer using interval
notation.)
Q...

3) If A = 3
1 and B
= 1 7
0
-2
5 -1
Find
a) BA
b) determinant
B
c) Adjoint A
d)
A-1
4) Using matrix method solve the following simultaneous
equations
5x – 3y = 1
2x – 2y = -2
5) Given that f(x) = 6x - 5 g(x) = 3x +
4 and h(x) = 4x – 6
2
Find:-
i)...

In the study of logarithns and exponentials we first learn about
one-to-one functions and inverse functions because the logarithm
and exonential functions are inverse functions. Many conceptsare
involved in the study of these two topics. Please demonstrate your
understanding of the concepts by following the discussion guideline
below: Start with a medium difficulty level function and then find
its inverse function (should take at least 3 steps) and write the
inverse function in terms of x. Name the original function...

In the study of logarithns and exponentials we first learn about
one-to-one functions and inverse functions because the logarithm
and exonential functions are inverse functions. Many conceptsare
involved in the study of these two topics. Please demonstrate your
understanding of the concepts by following the discussion guideline
below:
Start with a medium difficulty level function and then find its
inverse function (should take at least 3 steps) and write the
inverse function in terms of x. Name the original
function f(x)...

5. Part I
If f(x) = 2x 2 - 3x + 1, find f(3) - f(2).
A. 0
B. 7
C. 17
Part II
If G( x ) = 5 x - 2, find G-1(x).
A. -5x + 2
B. (x + 2)/5
C. (x/5) + 2
Please help me solve this problem and if you can please also
show or explain how you got that answer. Thank you! :)

Let g(x) = 21x^5 - 116x^4 + 186x^3 - 328x^2 + 369x + 60. Find
g'(x) and use this to find the stationary values of g(x). After
finding the critical values, determine any local extrema using the
FindMinimum and FindMaximum commands; state any critical values and
local extrema in a text cell (x-values only).
Please explain this is Wolfram Mathematica input terms! I got
most of this, but I dont know what to put for the critical values
or local...

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