Question

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)

Answer #1

Differentiating with respect to x

[f(0)=2, g(0)=4, f′(0)=12 and g′(0)= -2]

[Quotient rule:-

]

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...

f(x) =x2 -x
use f'(x)=lim h->0 f(x+h) - f(x)/h
find:
1. f '(x)
2. f '(2)
3. Find the equation of a tangent line to the given function at
x=2
4. f ' (-3)
5. Find the equation of a tangent line to the given function at
x=-3

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)

Consider the following functions
f(x) =x^2, g(x) = lnx, h(x) = cosx
For each of the following parts, you may use compositions,
products, and sums of thefunctions above, but no others. For
example, we can combine in the following waysh(g(x)) = cos(lnx), or
g(x)h(x) = lnxcosx, or g(x) +h(x) = lnx+ cosx
show how derivative rules apply to the function you came up
within order to produce the requested derivative.
1)A functionk(x) whose derivative is k′(x) = −tanx=
-(sinx/cosx)
2)...

Let h(x) = f (g(x) − (x^2 + 1)) . If f(0) = 3, f(2) = 5, f ' (0)
= −5, f ' (2) = 11, g(1) = 2, and g ' (1) = 4.
What is h(1) and h ' (1)?

If f(2) = 3, f'(2) = 5, g(2) = 1, and g'(2) = 4, find h'(x) and
r'(x) if h(x) = 2(f(x))3/2 and r(x) = g(x) + p g(x), and determine
the greater value between h'(2) and r'(2).

Find each of the following functions. f(x) = 4 − 4x, g(x) =
cos(x)
(a) f ∘ g and State the domain of the function. (Enter your
answer using interval notation.)
(b) g ∘ f and State the domain of the function. (Enter your
answer using interval notation.)
(c) f ∘ f and State the domain of the function. (Enter your
answer using interval notation.)
(d) g ∘ g and State the domain of the function. (Enter your
answer using...

For f(x) = x^2+6 and g(x) = x^2-5 find the following
functions.
a.) (f o g)(x)
b.) (g o f) (x)
c.) (f o g) (4)
d.) (g o f) (4)

Consider the following five utility functions.
G(x,y) = x2 + 3 y2
H(x,y) =ln(x) + ln(2y)
L(x,y) = x1/2 + y1/2
U(x,y) =x y
W(x,y) = (4x+2y)2
Z(x,y) = min(3x ,y)
In the case of which function or functions can the Method of
Lagrange be used to find the complete solution to the consumer's
utility maximization problem?
a.
H
b.
U
c.
G
d.
Z
e.
L
f.
W
g.
None.

The functions f(x) = –(x + 4)^2 + 2 and g(x) = (x − 2)^2 − 2
have been rewritten using the completing-the-square method. Is the
vertex for each function a minimum or a maximum? Explain your
reasoning for each function.

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