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
slava [35]
3 years ago
7

Suppose that we don't have a formula for g ( x ) g(x) but we know that g ( 1 ) = − 1 g(1)=-1 and g ' ( x ) = √ x 2 + 15 g′(x)=x2

+15 for all x x. (a) Use a linear approximation to estimate g ( 0.9 ) g(0.9) and g ( 1.1 ) g(1.1). (Round your answers to two decimal places.) g ( 0.9 ) ≈ g(0.9)≈ g ( 1.1 ) ≈ g(1.1)≈ (b) Are your estimates in part (a) too large or too small? Explain. The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie below the curve. Thus, the estimates are too small. The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie above the curve. Thus, the estimates are too large. The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie below the curve. Thus, the estimates are too small. The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie above the curve. Thus, the estimates are too large.
Mathematics
1 answer:
dezoksy [38]3 years ago
4 0

Answer:

g(0.9) ≈ -2.6

g(1.1) ≈ 0.6

For 1.1 the estimation is a bit too high and for 0.9 it is too low.

Step-by-step explanation:

For values of x near 1 we can estimate g(x) with t(x) = g'(1) (x-1) + g(1). Note that g'(1) = 1²+15 = 16, and for values near one g'(x) is increasing because x² is increasing for positive values. This means that the tangent line t(x) will be above the graph of g, and the estimates we will make are a bit too big for values at the right of 1, like 1.1, and they will be too low for values at the left like 0.9.

For 0.9, we estimate

g(0.9) ≈ 16* (-0.1) -1 = -2.6

g(1.1) ≈ 16* 0.1 -1 = 0.6  

You might be interested in
if all of the medians of a triangle were constructed, what would the point where they all intersect be called?
Lubov Fominskaja [6]

Answer:

i think its centroid not sure though.

Step-by-step explanation:

3 0
3 years ago
how much does a bag of wood chips weighs 12.4 pounds how much does a bad that contains .42 as many wood chips weigh
Law Incorporation [45]

Answer:

5.208 lbs

Step-by-step explanation:

12.4 lbs times 0.42 is 5.208 lbs

it is simple

3 0
3 years ago
Read 2 more answers
Which of the following always passes through a vertex of a triangle . choose all that apply.
Helga [31]

Just finished the test and the write answers are :

1) A,D,E

2)A,B

3)B,E

4) D

5) A

6) C

7) A

8) B

9) part A is C

Part B is A

Score 100%

7 0
3 years ago
Which is equivalent to (4xy – 3z)2, and what type of special product is it?
valina [46]
(4xy - 3z)²

(4xy - 3z)(4xy - 3z)
4xy(4xy - 3z) - 3z(4xy - 3z)
16x²y² - 12xyz -12xyz + 9z²

16x²y² - 24xyz + 9z², a perfect square trinomial.


5 0
3 years ago
Read 2 more answers
Solve.<br> 2x + 3 = 2x - 3
WINSTONCH [101]

Step-by-step explanation:

Respuesta:13

3 0
2 years ago
Read 2 more answers
Other questions:
  • Drag each figure to show if it is similar to figure shown or why it is not similar
    8·1 answer
  • How many solutions does this system of equations have? infinitely many exactly two exactly one none
    8·2 answers
  • What value of y makes the equation true? -7/12=y/-36
    15·1 answer
  • Think I know what the answer is but not sure. Hope someone can.help
    15·2 answers
  • Mary has 1/4 of a tank of gas.A quarter or a tank is equal to 5 gallons how many gallons does her tank hold
    7·1 answer
  • Please help me. I’ll mark brainliest!!!
    7·1 answer
  • The probability that a house in an urban area will develop a leak is 6%. If 10 houses are randomly selected, what is the probabi
    15·1 answer
  • Choose the equation below that represents the line passing through the point (−2, −3) with a slope of −6.
    5·2 answers
  • You will be marked brainlest
    14·2 answers
  • Factor the expression using the GCF.<br> 42 – 12 =
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!