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
Vedmedyk [2.9K]
1 year ago
6

Show that the function has at least one zero between x=1 and x=2

Mathematics
1 answer:
ANTONII [103]1 year ago
7 0

Answer:

See Below.

Step-by-step explanation:

We are given the function:

\displaystyle f(x) = 7x^5-9x^4-x^2

And we want to show that it has at least one zero between <em>x</em> = 1 and <em>x</em> = 2.

Because the function is a polynomial, it is everywhere continuous.

Evaluate the function at <em>x</em> = 1 and <em>x</em> = 2:

\displaystyle \begin{aligned} f(1) & = 7(1)^5 - 9(1)^4 - (1)^2 \\ \\ & = -3\end{aligned}

And:

\displaystyle \begin{aligned} f(2) & = 7(2)^5 - 9(2)^4 - (2)^2 \\ \\ & = 76 \end{aligned}

Therefore, because the function changes signs from <em>x</em> = 1 to <em>x</em> = 2 and is continuous on the interval [1, 2], by the intermediate value theorem, there must exist at least one zero in the interval.

You might be interested in
Answer I'll give brainliest to first one<br>10 points​
defon

Answer:

Have a splendiferous day...

Step-by-step explanation:

3÷12=¼

6÷10=⅗

7÷14=½

10÷11=⅚

2÷4=½

4÷16=¼

3÷24=⅛

18÷54=⅓

7 0
2 years ago
Read 2 more answers
The value of the figure's surface area is equal to the value of the figure's volume find the value of x. the picture is of recta
emmasim [6.3K]
Surface are of a rectangular prism = 2(l x w + l x h + w x h) = 2(10 x 3 + 10x + 3x) = 2(30 + 13x) = 60 + 26x

Volume of a rectangular prism = l x w x h = 10 * 3 * x = 30x

Since surface area = volume
60 + 26x = 30x
4x = 60
x = 15 in
7 0
3 years ago
Help me please, I have beeen trying to figure this out but I can’t
Ulleksa [173]

Answer:

M and N

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Dividing mixed numbers
Mars2501 [29]

\frac{9}{14}

8 0
3 years ago
Read 2 more answers
Simplify the expression. Write the answer using scientific notation. (5 x 102)−2
marissa [1.9K]
102 multiply 5 is equally to 610 so that's gonna be 6.10 I think
7 0
3 years ago
Read 2 more answers
Other questions:
  • What do Properties mean??
    14·2 answers
  • A loan given to people who are purchasing real estate is called a
    9·2 answers
  • Evaluate the function rule to find the range of each function for the domain.
    5·1 answer
  • Find the perimeter of the following shape, rounded to the nearest tenth: Shape ABCD is shown. Point A is at negative 3, 5. Point
    10·1 answer
  • please help me vote brainiest
    9·1 answer
  • George bought 5 and 3/4 dozen muffins. How many muffins does he have?
    7·2 answers
  • Consider the following sets of matrices: M2(R) is the set of all 2 x 2 real matrices; GL2(R) is the subset of M2(R) with non-zer
    7·1 answer
  • What would the solution be for x <br> x-15=y
    9·1 answer
  • What is 3/14 divided by 7/10
    7·2 answers
  • Find an expression for the nth term (tn) in each of the following sequence:
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!