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
Ratling [72]
2 years ago
6

Verify that the function

="g(x)=2x^3-3x+1" align="absmiddle" class="latex-formula"> satisfies the three hypotheses of Rolle’s Theorem on the interval [0,2].
Mathematics
1 answer:
ch4aika [34]2 years ago
5 0

Lets check if the three conditions hold.

<u>1 : Continuity of g on the interval [0,2]</u>

First, g(x) is a continuous function on R, as the sum of a cubic function wich is continuous on R, and a linear polynomial of the form ax + b which is also continuous on R. Finally g is also continuous on the interval [0,2]

<u>2 : Differentiable on the same interval</u>

Since the cubic function and the linear polynomial one are differentiable on R, g also is differentiable and particularly on the interval [0,2]

Also we have g'(x) = 2*3*x² - 3 = 6x² - 3

<u>3 : Do we have g(0) = g(2) ?</u>

Lets compute g(0) = 2*0^3 - 3*0 + 1 = 1

And g(2) = 2*2^3 - 3*2 + 1 = 2 * 8 - 6 + 1 = 16 - 6 + 1 = 11

Since g(0) ≠ g(2), Rolle's theorem is not applicable. Thus unfortunately, we can not conclude that there exist c ∈ (0,2) such that f'(c) = 0

You might be interested in
A ball is launched into the sky at 48 feet per second from a building 48 feet tall. The equation for the ball’s height h at time
kkurt [141]

Answer:

4 seconds I believe

Step-by-step explanation:

3 0
3 years ago
Deon drove 16 miles which is one fourth of the way home what’s the total length of the drive
svetlana [45]
64 miles

If 16 is 1/4 of the total distance, then x (the total distance) will be 4/4. To get 1/4 to equal 4/4, you multiply it by 4. Therefore you can multiply 16 by 4 to get 64 as the answer.
6 0
2 years ago
Read 2 more answers
Please help. 10 points. Please do not guess. Guesses will be reported. Thanks
Allushta [10]

The intersecting secant-tangent theorem says that

AP^2=PT\cdot TO

where T is the point at which line segment PO touches the circle. Similarly,

BP^2=PT\cdot TO

so we have

AP^2=BP^2\implies AP=BP

OP is of course as long as itself, and AO and BO are radii of the same circle so they have the same lengths.

This means triangles APO and BPO are congruent, which means angles APO and BPO are congruent, so angle APB is bisected by PO.

8 0
3 years ago
I need help ASAP !!!!!
s2008m [1.1K]

Answer:

the answer is -352..........

6 0
2 years ago
Answer correctly for brainly (not 4
vaieri [72.5K]

Hello there again. I have your answer: Solve for x by simplifying both sides of the equation, then isolating the variable. x = −8

8 0
2 years ago
Read 2 more answers
Other questions:
  • Suppose SAT Writing scores are normally distributed with a mean of 498 and a standard deviation of 108. A university plans to aw
    9·1 answer
  • And object Weighs a quarter of a kilogram . I add one half of a kilogram to the object. I take 200g off. I double the mass of th
    9·1 answer
  • If (6^0)^x = 1 , what are the possible values of x? Explain your answer. (5 points)
    15·2 answers
  • A line passes through (9,-8) and has a slope of negative 4/3
    11·1 answer
  • Max drove 203 miles in 3.5 hours. What was his average speed in miles per hour?
    14·1 answer
  • You must score at least 50 points. You currently have
    6·2 answers
  • Find the equation of the line. Use exact numbers
    9·1 answer
  • For the equation, complete the given ordered pairs.<br><br> 3x-y=4<br><br> {0,_} [1,_} {_,4}
    6·1 answer
  • cooper got 60% off a pair of shoes. if the sale price of the shoes was $19.75 before tax, what was the original
    13·1 answer
  • Question Help A 156-inch board is cut into two pieces. One piece is two times the length of the other. Find the length of the sh
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!