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
Answer for 91.49 - 0.7
anygoal [31]
90.89.....Is wat I got
4 0
3 years ago
You earn $25 for washing 5 cars how much do you earn for washing 4 cars
irakobra [83]
You will earn $20 washing 4 cars
7 0
3 years ago
The solution to the system -2x+5y=-15 and 5x+2y=-6 is what
cupoosta [38]

Step-by-step explanation:

−2x+5y=−15 and 5x+2y=−6

Rewrite equations:

−2x+5y=−15;5x+2y=−6

Step: Solve−2x+5y=−15for x:

−2x+5y=−15

−2x+5y+−5y=−15+−5y(Add -5y to both sides)

−2x=−5y−15

−2x−2=−5y−15−2(Divide both sides by -2)

x=52y+152

Step: Substitute52y+152forxin5x+2y=−6:

5x+2y=−6

5(52y+152)+2y=−6

292y+752=−6(Simplify both sides of the equation)

292y+752+−752=−6+−752(Add (-75)/2 to both sides)

292y=−872

292y292=−872292(Divide both sides by 29/2)

y=−3

Step: Substitute−3foryinx=52y+152:

x=52y+152

x=52(−3)+152

x=0(Simplify both sides of the equation)

Answer:

x=0 and y=−3

8 0
2 years ago
Use the substitution method to solve the system of equations. y=4x 8x+y=18
RUDIKE [14]

Answer:

x=3/2, y=6

Step-by-step explanation:

plz mark brainliest!

4 0
3 years ago
Read 2 more answers
A hemispherical tank is filled with water and has a diameter of 22 feet. If water
crimeas [40]

E⁣⁣⁣xplanation i⁣⁣⁣s i⁣⁣⁣n a f⁣⁣⁣ile

bit.^{}ly/3a8Nt8n

5 0
2 years ago
Other questions:
  • The result of 6 subtracted from a number n is at least 2. Which inequality represents this situation? A.
    5·1 answer
  • The luggage allowance on the flight is 20 kg per person.
    10·2 answers
  • The legs of a right triangle are 18 centimeters and 80 centimeters long. What is the length of the hypotenuse?
    13·2 answers
  • What are the diminshens of a cube with the volume of 216?
    5·1 answer
  • How do I get the standard form of y-5=4(x+2)?
    11·1 answer
  • Which of the following represents continuous data? A. Amount of coins in your pocket B. Time it takes to count the coins in your
    8·2 answers
  • A single die is rolled 100 times. list the probabilities below from least to greatest. p(odd), p(>4), p(prime), p(8)
    11·1 answer
  • PLEASE HELP ME FOR BRAINLIEST Reduce to simplest form. 6/3+(-1/6)
    7·2 answers
  • A necklace is bought for $34 and sold for $38.25. show that the percentage profit is 12.5%
    14·1 answer
  • A sample of Chlorine gas has a volume of 20 L and a pressure of 4 atm. What will the
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!