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
morpeh [17]
3 years ago
7

4. Consider the function g(x) = 2x^2 - 4x+3 on the interval [-1, 2]

Mathematics
1 answer:
yanalaym [24]3 years ago
7 0

Hi there!

A.) Begin by verifying that both endpoints have the same y-value:

g(-1) = 2(-1)² - 4(-1) + 3

Simplify:

g(-1) = 2 + 4 + 3 = 9

g(2) = 2(2)² - 4(2) + 3 = 8 - 8 + 3 = 3

Since the endpoints are not the same, Rolle's theorem does NOT apply.

B.)

Begin by ensuring that the function is continuous.

The function is a polynomial, so it satisfies the conditions of the function being BOTH continuous and differentiable on the given interval (All x-values do as well in this instance). We can proceed to find the values that satisfy the MVT:

f'(c) = \frac{f(a)-f(b)}{a-b}

Begin by finding the average rate of change over the interval:

\frac{g(2) - g(-1)}{2-(-1)} = \frac{3 - 9 }{2-(-1)} = \frac{-6}{3} = -2

Now, Find the derivative of the function:

g(x) = 2x² - 4x + 3

Apply power rule:

g'(x) = 4x - 4

Find the x value in which the derivative equals the AROC:

4x - 4 = -2

Add 4 to both sides:

4x = 2

Divide both sides by 4:

x = 1/2

You might be interested in
14х – бу = 66<br> Find the slope and y intercept
Pepsi [2]

Answer:

Slope: 7/3 | Y Intercept: -11

Step-by-step explanation:

To translate this equation into a slope-intercept form equation, we can subtract 14x on both sides. This leaves us with: -6y = -14x + 66.

Now, all that is preventing us from putting it into the correct from is -6, so we can simply divide -6 on both sides. Using this operation, we get: y = 14x/6 + -11. The coefficient of x in this problem stands for slope, so the slope is: 14/6 or 7/3. The constant stands for y intercept, so that is -11.

Hope you understood and do well!

4 0
4 years ago
Write the equation of the line with the given slope and the given point.<br><br> y = ?
Naddika [18.5K]

Answer:

y=x+8

Step-by-step explanation:

y=x+b

That is the equation with only the slope, however, we can use the point (-4,4) to find the y-intercept

4=-4+b

Add 4 both sides:

8=b

Thus the equation is y=x+8

Hope this helps!

3 0
3 years ago
Read 2 more answers
Pls help plssssssssssss
frutty [35]
The correct and right answer is 181m
3 0
3 years ago
Jacelin was paid $50 after a day of babysitting. She watched the children from 8am until 4pm. What is the unit rate of her earni
taurus [48]

Answer:

The unit rate of her earnings is 12.5

Step-by-step explanation:

50 divided by 9 = 12.5

She makes $12.50 an hour.

5 0
3 years ago
Caroline withdrew $4 from her banking account each day for 7 days. What was the overall change in her account?
kkurt [141]
She withdrew $ 4 from her account each day for 7 days...
(4 * 7) = 28

so she withdrew a total of $ 28

her overall change in her account would be -28...it would be $ 28 dollars less
6 0
3 years ago
Other questions:
  • Explain the process for finding the product of two integers
    7·2 answers
  • Suppose 123 people voted for Danny. If 55 of the votes were from girls, what would be the ratio of votes from girls to votes fro
    14·2 answers
  • An ancient artifact was recently discovered, but due to rust and corrosion, only 75 grams of the original item remained. Based o
    9·2 answers
  • Help ASAP with these
    8·1 answer
  • Mr. Barclay sold goods for $21 and lost a percent equal to the number of dollars he paid for the goods. How much did the goods c
    10·1 answer
  • The projected number of employed writers and authors in 2016 is 153,000. 12.4% of those will have some college experience but no
    15·1 answer
  • A circle has a diameter of 10 feet. What is the area of the circle? Leave answers in terms of pie
    9·2 answers
  • The priduct of seven and p
    11·1 answer
  • Select all that apply.
    9·1 answer
  • Fuel for the reasearch vessels will be stored in a cylindrical tank with a radius of 10 meters and a height of 5 meters. Using a
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!