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
Gre4nikov [31]
3 years ago
7

Find the Horizontal Tangent for x^3/3+3x^2-16x+9

Mathematics
1 answer:
bazaltina [42]3 years ago
3 0

Answer:

The two horiz. tang. lines here are y = -3 and y = 192.

Step-by-step explanation:

Remember that the slope of a tangent line to the graph of a function is given by the derivative of that function.  Thus, we find f '(x):

f '(x) = x^2 + 6x - 16.  This is the formula for the slope.  We set this = to 0 and determine for which x values the tangent line is horizontal:

f '(x) = x^2 + 6x - 16 = 0.  Use the quadratic formula to determine the roots here:  a = 1; b = 6 and c = -16:  the discriminant is b^2-4ac, or 36-4(1)(-16), which has the value 100; thus, the roots are:

      -6 plus or minus √100

x = ----------------------------------- = 2 and -8.

                         2

Evaluating y = x^3/3+3x^2-16x+9 at x = 2 results in y = -3.  So one point of tangency is (2, -3).  Remembering that the tangent lines in this problem are horizontal, we need only the y-coefficient of (2, -3) to represent this first tangent line:  it is y = -3.

Similarly, find the y-coeff. of the other tangent line, which is tangent to the curve at x = -8.  The value of x^3/3+3x^2-16x+9 at x = -8 is  192, and so the equation of the 2nd tangent line is y=192 (the slope is zero).


You might be interested in
Equivalent ratio for 10/24<br><br><br> PLEASE NOW HURRY
Luden [163]

Step-by-step explanation:

fraction 10/24

you want the ratio

answer is 5:12

if you want the explanation look below

Step One: Reduce the fraction

10/24

=

5/12

Step Two: Rewrite as a ratio

5/12 = 5 : 12

6 0
3 years ago
Read 2 more answers
If the mean of the data below is 3.8, find m<br>x 1 2 3 4 5 6<br>f 1 4 7 m 6 3​
zloy xaker [14]

Answer:

m = 1.8

Step-by-step explanation:

Given data is as follows :

x 1 2 3 4 5 6

f 1 4 7 m 6 3​

We need to find the value of m if the mean of the data is 3.8.

Mean = sum of observations/no. of observations

So,

3.8=\dfrac{1+4+7+m+6+3}{6}\\\\22.8=21+m\\\\22.8-21=m\\\\m=1.8

So, the value of m is equal to 1.8.

8 0
3 years ago
Which multiplication expression is eqeul to 3/5 ÷ 1/2
eduard

Answer:

Lets solve = 3/5 ÷ 1/2

3/5 ÷ 1/2

= 3/5 × 2/1

= 3 × 2/5 × 1

= 6/5

In mixed fraction its

1 \frac{1}{5}

____________________

Now lets solve "a" option

3/5 × 2

= 3 × 2/5 × 1

= 6/5

In mixed fraction

1 \frac{1}{5}

So option a = 3/5 x 2/1 is ur answer

8 0
2 years ago
Read 2 more answers
Just give answers to blanck ones just give me The answers cause I don't want no explaining because I'm Savage
Airida [17]
Omg wow bruh #savageaf
6 0
3 years ago
Read 2 more answers
at the movie theatre, child admission is $5.20 and adult admission is $9.00. on Monday, 132 tickets were sold for a total sales
kakasveta [241]

Answer:

That day 51 child tikets were sold

Step-by-step explanation:

To do this problem we have to make 2 equations, one that represents the number of entries and the other that represents the money

x = child tickets

y = adult tickets

x + y = 132

x * $5.20 + y * $9.00 = $994.20

First we have to solve for the x in the first equation

x + y = 132

x = 132 - y

Now we replace the x with (132 - y) in the second equation

x * $5.20 + y * $9.00 = $994.20

(132 - y) * 5.20 + y * 9.00 = 994.20

686.4 - 5.2y + 9y = 994.2

-5.2y + 9y = 994.2 - 686.4

3.8y = 307.8

y = 307.8/3.8

y = 81

We replace y with its value in the first equation

x = 132 - y

x = 132 - 81

x = 51

That day 51 child tikets were sold

6 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following is equivalent to the equation below
    8·1 answer
  • 40. A catering chef is making a large quantity
    5·1 answer
  • In a shipment of 71 vials, only 13 do not have hairline cracks. If you randomly select 2 vials from the shipment, what is the pr
    7·1 answer
  • HELP! <br> Which of the following is a correct interpretation of the expression 1+6?
    7·2 answers
  • URGENT SIMPLE TRIANGLE AND SINES PROBLEM ONLY ASKING FOR A WORD EXPLANATION: PLEASE HELP!!
    8·1 answer
  • Help plz can’t figure this out
    9·2 answers
  • Svetlana's hair is 4 centimeters long. Her hair grows 1.5 centimeters per month. Svetlana wants her hair to grow so that it is a
    7·1 answer
  • Find the length of the missing side. Leave your answer in simplest radical form.
    12·1 answer
  • A bag Contains five blue marbles two green marbles and three yellow marbles what is the probability of Choosing one Green marble
    8·1 answer
  • Find x. Round your answer to the nearest integer.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!