1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tiny-mole [99]
3 years ago
11

Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x. (

Mathematics
1 answer:
True [87]3 years ago
5 0
So it tells us that g(3) = -5 and g'(x) = x^2 + 7.

So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))

now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16 

Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84

So we have our linear approximation for the two. 

If you wanted to, you could check your answer by finding g(x).  Since you know g'(x), take the antiderivative and we will get 
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35

So just to check our linear approximations use that to find g(2.99) and g(3.01)

g(2.99) = -5.1597
g(3.01) = -4.8397

So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer.  Not a bad method if you ever need to use it. 
You might be interested in
Multiply.
alina1380 [7]

Answer:

2/4 or 1/2

Step-by-step explanation:

i used a numbers chart to break the numbers down.

5 0
2 years ago
Bianca filled 2 same-sized jars with flavored popcorn as a gift. She wants to glue a piece of ribbon around the edge of each lid
dybincka [34]
I think it is 177.4728 

but im not sure let me check


7 0
3 years ago
Read 2 more answers
Sheila is going to divide a 38-inch piece of ribbon into 5 equal pieces. She says each piece
DENIUS [597]

Sheila is incorrect! I think what she did is think the 38 was actually a 35, which WOULD of made her statement true, but since it's 38, she's very incorrect. Sheila should be using the quotient for the size of each piece. 38 divided by 5 is 7.6. The correct answer is 7.6 inches.

5 0
3 years ago
Find the obtuse angle the line y-2x=7 makes with the x- axis
Kazeer [188]
In analytical geometry, there are already derived equations to find the distance of lines and points as well as the angle made between two lines. As special case is when the other line is one of the coordinate axis. Then, the formula can be simplified to

tan θ =m, where m is the slope of the equation

In the next step, we also incorporate operations of calculus. Since the slope is equal to Δy/Δx, this is equivalent to dy/dx in calculus. Therefore, you can find the slope by differentiating the equation in terms of x.

<span>y-2x=7
y = 2x+7
dy/dx = 2 =m

So,

tan </span>θ = 2
θ = tan⁻¹(2)
θ = 63.43°
5 0
3 years ago
1: In order to solve the inequality -1/4 x &gt; 8, which of the following steps must be done?
pogonyaev

Answer:

Step-by-step explanation:

-1/4x>8

x>8/(-1/4)

x>(8/1)(-4/1)

x>-32/1

x>-32

x<-32

The answer is D.

--------------------------

-3t+7>=9

-3t>=9-7

-3t>=2

t>=2/-3

t>=-2/3

t<=-2/3

The answer is A.

3 0
3 years ago
Other questions:
  • How can u enlarge or reduce a drawing proportinally
    13·2 answers
  • There are 13 teams of cheerleaders at a competition. The order of performance is determined at random. What is the probability t
    8·1 answer
  • How would you find the missing x and y values if you don’t have a model or equation to go by?
    9·1 answer
  • What are the steps in solving the algibia math question 3m + 2/5 ; m =2/3
    13·1 answer
  • All of question 2 and 3
    7·1 answer
  • Describe the patter and find the next two terms of each sequence <br> 5,1,7,0,9,-1,11
    13·1 answer
  • Pls answer this fast
    14·1 answer
  • A user car dealer brought a car for $12,000 and wants to sell it at a 15% profit. How much should he sell the car for?
    13·2 answers
  • 8 cm<br> 5 cm<br> 10 cm<br> 12 cm
    5·1 answer
  • Step by Step What do I do
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!