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
What is 7.2 times 10 to the 7th power times 14.6 x 10 to the 5th power?
Alexxx [7]

7 x 10^{7}  times 14.6 x10^{5}

<em>Multiply 7 and 14.6 and add exponents</em>

Final Answer 102.2 and 10^{5}

hope that helps :)

6 0
3 years ago
Read 2 more answers
I need help answering this question...
koban [17]
We need to solve how much it cost to paint a room with are 459 ft² given that a room with an area of 306 ft² costs $72. The solution is shown below:
Cost per area = $72 / 306 ft²
Cost per area = $0.2353 / ft²

Solving the cost for the similar room:
Costs = $0.2353 * 459 ft²
Costs = $108

The answer is $108.
4 0
3 years ago
A bag contains white matarles and red marables,126 in total.The number of whit marables is 6 more than 5 than 5 times the number
denis-greek [22]

Answer:106

Step-by-step explanation:

Let number of white marbles be w

Let number of red marbles be r

w+r = 126---------1

w = 6 +5r-----------2

Put eqn 2 in eqn 1

6+ 5r + r = 126

6 + 6r = 126

6r = 120

r = 20

w = 6 +5r =6+100

= 106

3 0
3 years ago
Solving quadratic equation<br>7r^2-14=-7
Gala2k [10]
I hope this helps you

7 0
3 years ago
In a large population, 53 percent of the people have been vacinated. If 4 people are randomly selected, what is the probability
MArishka [77]

Answer:

4/57

Step-by-step explanation:

Prob=DC/SS

=4/53+4

=4/57

3 0
3 years ago
Other questions:
  • *44 POINTS*
    5·1 answer
  • Solve using trigonometry. Round to the nearest degree.<br> 16<br> х<br> 30
    10·1 answer
  • What is 3/8 divided by 3/4 ​
    5·1 answer
  • Will mark brainliest please help
    6·1 answer
  • The Egyptians used a ramp that could hold 1,000 pounds. If 6 people got on the ramp and they weighed 780 pounds total. What perc
    7·1 answer
  • What is the value of the angle marked with x?
    6·2 answers
  • Show the numbers 0.29,0.2,1/4,1/10,and 16% from least to greatest
    7·1 answer
  • roberts mom gave him $9 to buy groceries. she told him to buy a loaf of bread and as many quarts of milk as he could with the mo
    5·1 answer
  • What is the volume in cubic feet of a cylinder with a height of 3 feet and base radius of 2
    5·1 answer
  • ANSWER FAST FAST FAST FAST FAST answer here r u 11 and a girl and live in etna ohio say yes for 100 points!!
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!