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
andrew11 [14]
3 years ago
15

Use the following graph to estimate the rate of change of the function at x=0.6 using the points (0,0) and (1,−0.5)

Mathematics
1 answer:
svetoff [14.1K]3 years ago
4 0

Answer:

The rate of change of the function at x = 0.6 is approximately -0.72

Step-by-step explanation:

The given information from the graph are;

Points (0, 0) and (1, -0.5)

We have that the graph is that of a cubic function, therefore;

f(x) = ax³ + bx² + cx + d

At f'(x) at  (0, 0) and (1, -0.5) = 0 gives;

3ax² + 2bx + c = 0

∴ c = 0

Also

ax³ + bx² + cx + d = 0

d = 0

We have

3a(1)² + 2b(1) + 0 = 0

3·a + 2·b = 0..............(1)

a(1)³ + b(1)² + c(1) + d = -0.5

a + b + 0×(1) + 0 = -0.5

a + b = -0.5..........(2)

Multiplying equation (2) by 2 and subtracting it from equation (1) gives;

2 × (a + b = -0.5) = 2·a + 2·b = -1

3·a + 2·b - (2·a + 2·b) = 0 - (-1) = 0 + 1 = 1

a = 1

From

a + b = -0.5, we have;

1 + b = -0.5 = 0

b = -0.5 - 1 = -1.5

The equation becomes

f(x) = x³ - 1.5·x²

The rate of change of the function at x = 0.6 is therefore given as follows;

f'(x) = 3 × x² - 2 × (1.5)·x = 3·x² - 3·x

At x = 0.6, we have;

f'(0.6) = 3·(0.6)² - 3·(0.6)

f'(0.6) = 3×0.6² - 3×0.6 = -0.72

The rate of change of the function at x = 0.6 ≈ -0.72

You might be interested in
Which expression is a rational number? A) ( 25 + 25 )2 B) ( 25 + 50 )2 C) ( 50 + 75 )2 D) ( 25 + 72 )2
tigry1 [53]
I believe it's a hope it helps
6 0
3 years ago
What is the equivalent expression for 2x + 8y​
klio [65]

If this helps you consider making it brainliest as it helps me out.

2(x+4y) is the equivalent expression.

Let’s say x = 1 and y = 2

Then 2x + 8y would be 18

Same thing for 2(x+4y)

Hope this helps!

7 0
2 years ago
Read 2 more answers
Prove that√P is irrational for any prime number P​
Luda [366]

Answer:

Step-by-step explanation:

I’m not sure if this is super accurate, but since P is prime, the only factors it has is 1 and itself, meaning that the square root of it will be irrational

3 0
3 years ago
What’s the positive square root of 9
vredina [299]

Answer:

3

Step-by-step explanation:

Three times three equals nine. Or you can just go by one times one, two times two, three times three.

3 0
2 years ago
Read 2 more answers
3⁄2 c + 23 = 38<br><br> can you help me find out what c is pretty please
kolbaska11 [484]

Answer:

C=10

Step-by-step explanation:

To solve this problem, first, you have to isolate it on one side of the equation. Remember, isolate c on one side of the equation.

3/2c+23-23=38-23 (subtract 23 from both sides.)

38-23 (solve.)

38-23=15

3/2c=15

2*3/2c=15*2 (multiply 2 from both sides.)

15*2 (solve.)

15*2=30

3c=30

3c/3=30/3 (divide by 3 from both sides.)

30/3 (solve.)

30/3=10

c=10

6 0
2 years ago
Other questions:
  • The attendances at the high school basketball games seems to be affected by the success of the team. The graph below models the
    8·1 answer
  • How much is 1 foot line of quarters worth
    7·1 answer
  • Which function has an inverse that is also a function?
    14·1 answer
  • Is there someone that is on here that will help me with my geometry because I'm not getting any of this, please?
    7·2 answers
  • PLEASE HURRY<br> which ordered pair represents point D
    6·2 answers
  • The quotient of x and 9 is greater than 27
    5·1 answer
  • If Benito is selecting samples of five values from the table, which row will result in the greatest mean? Population Data Row 1
    14·2 answers
  • The second term of arithematic proggresions 7. and the sum of the first four termd is 12 find
    9·1 answer
  • 20 POINTS
    12·1 answer
  • BRAINLIEST TO PERSON WHO HELPS
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!