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
Pls help and give steps pls I give brainliest thank uuuu
krek1111 [17]

Answer: 42 cm to the power of 3

Step-by-step explanation: L x w x h

3 x 7 x 2

21 x 2

42

6 0
3 years ago
Read 2 more answers
Rectangular field has a total perimeter of 128 feet. The width is
dsp73

Answer:

<h3>The length is 44 feet</h3><h3>The width is 20 feet</h3>

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

Perimeter = 128 feet

The width is 24 feet less than the length is written as

w = l - 24

128 = 2l + 2( l - 24)

128 = 2l + 2l - 48

Group like terms

4l = 176

Divide both sides by 4

l = 44

The length is 44 feet

Substitute l = 44 into w = l - 24

w = 44 - 24

w = 20

The width is 20 feet

Hope this helps you

5 0
3 years ago
Would you be more or less likely to take a job in which the type of work is enjoyable to you? Why?
OverLord2011 [107]
More likely because you are doing a job that you enjoy doing.
3 0
2 years ago
What is the scale factor of this dilation?
Mandarinka [93]

Answer:

2/3

Step-by-step explanation:

8 0
3 years ago
What is the equation of the line that is perpendicular to 9x+3y=36 and passes through the point (6,2)?
Fofino [41]
9x+3y=36

3y=-9x+36

y=-3x+36

For lines to be perpendicular their slopes must be negative reciprocals of each other...mathematically:

m1*m2=-1 and in this case for a line to be perpendicular to y=-3x+36 that line must have a slope of:

-3m=-1, m=1/3 so

y=x/3+b, and using point (6,2) we can solve for b, the y-intercept...

2=6/3+b

2=3+b

b=-1 so the perpendicular line passing through the point (6,2) is:

y=x/3-1 or more neatly...

y=(x-3)/3
7 0
2 years ago
Read 2 more answers
Other questions:
  • #10
    9·1 answer
  • How does the area of the triangle relate to the area of the square? Please Explain!!! I really don't get it!
    14·1 answer
  • Which of the following is an undefined term? <br> Angle <br> Line <br> Ray <br> Vertex
    12·2 answers
  • Triangle ABC is graphed on a plane. Within the triangle, point A(−6,8), point B(−6,2) and point C(1,2). If △ABC is reflected ove
    15·1 answer
  • (19x² + 12x+12) + (7X2 + 10x +13)
    12·1 answer
  • I need help on this ASAP no fofo answers
    10·1 answer
  • Function? {(10, 20), (11, 22), (11, 24), (13, 26)} ​
    12·2 answers
  • PLEASE HELP THIS IS DUE BY 10 MINUTES
    14·1 answer
  • What is the equation of the line whose graph is shown below?<br> у<br> 8<br> -7<br> х
    5·1 answer
  • A satellite travels from Earth to the moon (238,905 miles), then from the moon to Mars (48,340,732 miles) and finally from Mars
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!