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
Romashka-Z-Leto [24]
2 years ago
12

Determine whether Rolle's Theorem can be applied to f on the closed interval

Mathematics
2 answers:
notsponge [240]2 years ago
8 0

Rolle's theorem is applicable if f(a)=f(b) and $f$ is differentiable in $(a,b)$

since it's polynomial function, it's always continuous and differentiable..

and you can easily check that $f(0)=f(-3)=0$

so it is applicable.

now, $f'(x)=-2x+3=0 \implies x=\frac32$

there is only once value (as you can imagine, the graph will be downward parabola)

Ierofanga [76]2 years ago
6 0

Answer:

Yes, Rolle's theorem can be applied

There is only one value of c such that f'(c) = 0, and this is c = 1.5 (or 3/2 in fraction form)

Step-by-step explanation:

Yes, Rolle's theorem can be applied on this function because the function is continuous in the closed interval (it is a polynomial function) and differentiable  in the open interval, and f(a) = f(b) given that:

f(0)=-0^2+3\,(0)=0\\f(3)=-3^2+3\,(3)=-9+9=0

Then there must be a c in the open interval for which f'(c) =0

In order to find "c", we derive the function and evaluate it at "c", making the derivative equal zero, to solve for c:

f(x)=-x^2+3\,x\\f'(x)=-2\,x+3\\f'(c)=-2\,c+3\\0=-2\,c+3\\2\,c=3\\c=\frac{3}{2} =1.5

There is a unique answer for c, and that is c = 1.5

You might be interested in
D Question 5 5) A bag contains colored paper clips. 2 clips are green 4 clips are orange 2 clips yellow A paper clip will be ran
patriot [66]

Answer:

0.125

green

Step-by-step explanation:

Since we know that there is 8 clips (2+2+4) and then we take 4/8 as a decimal and we then get 0.125

6 0
3 years ago
Read 2 more answers
Marlin davies buys a truck for 28,000. In three years , the car depreciates 48% in value how much is the car worth in three year
Scrat [10]
$28,000
 X  48%
-----------
$13,440

The truck would be worth $13,440 by the end of the 3 year time span. Hope this helps!

5 0
2 years ago
Divide: 6 ÷ 1
fredd [130]

Answer:

One-sixth times StartFraction 2 over 1 EndFraction

5 0
2 years ago
Read 2 more answers
Which national legislature has themost members?
AfilCa [17]
China has the most members.
8 0
3 years ago
Cosx+1/sin^3x=cscx/1-cosx
ANTONII [103]
<span> I am assuming you want to prove:
csc(x)/[1 - cos(x)] = [1 + cos(x)]/sin^3(x).

 </span>
<span>If we multiply the LHS by [1 + cos(x)]/[1 + cos(x)], we get:
LHS = csc(x)/[1 - cos(x)]
= {csc(x)[1 + cos(x)]/{[1 + cos(x)][1 - cos(x)]}
= {csc(x)[1 + cos(x)]}/[1 - cos^2(x)], via difference of squares
= {csc(x)[1 + cos(x)]}/sin^2(x), since sin^2(x) = 1 - cos^2(x).

 </span>
<span>Then, since csc(x) = 1/sin(x):
LHS = {csc(x)[1 + cos(x)]}/sin^2(x)
= {[1 + cos(x)]/sin(x)}/sin^2(x)
= [1 + cos(x)]/sin^3(x)
= RHS.

 </span>
<span>I hope this helps! </span>
8 0
3 years ago
Other questions:
  • a rectangle has an area of 30 square meters and a perimeter of 34 meters. what are the dimensions of the rectangle?
    5·2 answers
  • If the shortest leg for two right triangles is two-thirds the size of the of the shared hypotenuse then what is the length of th
    7·2 answers
  • In your own words, explain the place value relationship when the same two digits are next to each other in a multi digit number.
    9·1 answer
  • When 47 is added to a number the result is 37 less than 7 times the number.
    13·1 answer
  • a jar of natural peanut butter normally costs $4.00.Today it's on sale for 3.60. What is the percentage of this discount?
    10·1 answer
  • Identify any congruent figures in the coordinate plane. explain.
    14·1 answer
  • Solve the equation a = m - n for the variable n. *
    13·1 answer
  • HELPPP!!! ILL GIVE YOU THE BRAINLIEST IF YOU ANSWER LESS THAN 5 MINS. If APQR - ASTU, which statement must be true?
    14·1 answer
  • (1) 16 liters of kerosene is needed for 12 stoves 14
    6·2 answers
  • Pls help will give brainliest
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!