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
A number cube was rolled as part of an experiment. The results are displayed in the table below. What is the best explanation of
Mars2501 [29]

Answer:

The outcome table was not given. But find below how to find the experimental probability

Step-by-step explanation:

Experimental Probability = number of times you rolled a three  /   the number of times you rolled the die itself.

4 0
3 years ago
Read 2 more answers
Michelle drove a total of 57.8 kilometers on saturday. she drove 23.5 kilometers from her house to the park. her next stop was t
zloy xaker [14]
47.5 need this to extend my answer
5 0
3 years ago
Solve the one-variable equation using the distributive property and properties of equality.
Tanzania [10]

Answer:

a=6

Step-by-step explanation:

-6(2+(6)=-48

-6(2+6)=-48

(-6X2)+(-6+6)=-48

(-12)+(-36)=-48

-48=-48

They are equal. Tell me if I made a mistake. Thanks!

6 0
3 years ago
Read 2 more answers
There are ways to find the area under a normal curve.<br><br> True or false?
Mrrafil [7]

Your answer would be false.

7 0
3 years ago
Read 2 more answers
Katie's bank statement shows a closing balance of $178.11. There are no outstanding checks or deposits. Her checkbook shows a ba
castortr0y [4]
Overdraft fee in the amount of 20.00
7 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following is a solution to the inequality y &lt; –2x + 3?
    12·1 answer
  • Chris's pay went from $20/hr to $25/hr after his first evaluation. After his second evaluation his pay was raised to $33/hr. Whe
    13·1 answer
  • Equation of a line passing through 2,5 with a slope of -1
    6·1 answer
  • Does 2 times 36 equal 3 times 24
    9·1 answer
  • Milo has a collection of DVDs. Out of 45 DVDs, 40% are comedies and the remaining are action-adventures. How many action-adventu
    14·1 answer
  • Find the GCF of the polynomial, 20ab³ + 16a²b + a
    7·1 answer
  • The equation of a line is p is 2x + 3y = 3, and the equation of line q is 2x - 3y = 0. Lines P and q have same y -intercept
    13·1 answer
  • Plz Help FAST!!! Proportional relationship Study Island
    5·1 answer
  • Solve the quadratic equation: x^2+ 2x + 7 = 21
    12·1 answer
  • 1. The spinner shown has six equal-size sections and is spun twice. What is the probability that the product of the number spun
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!