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
ziro4ka [17]
2 years ago
11

Find a point on the curve x^3+y^3=11xy other than the origin at which the tangent line is horizontal.

Mathematics
1 answer:
attashe74 [19]2 years ago
3 0

Compute the derivative dy/dx using the power, product, and chain rules. Given

x³ + y³ = 11xy

differentiate both sides with respect to x to get

3x² + 3y² dy/dx = 11y + 11x dy/dx

Solve for dy/dx :

(3y² - 11x) dy/dx = 11y - 3x²

dy/dx = (11y - 3x²)/(3y² - 11x)

The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when

11y - 3x² = 0

or

y = 3/11 x²

(provided that 3y² - 11x ≠ 0)

Substitute y into into the original equation:

x³ + (3/11 x²)³ = 11x (3/11 x²)

x³ + (3/11)³ x⁶ = 3x³

(3/11)³ x⁶ - 2x³ = 0

x³ ((3/11)³ x³ - 2) = 0

One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with

(3/11)³ x³ - 2 = 0

(3/11 x)³ - 2 = 0

(3/11 x)³ = 2

3/11 x = ³√2

x = (11•³√2)/3

Solving for y gives

y = 3/11 x²

y = 3/11 ((11•³√2)/3)²

y = (11•³√4)/3

So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).

You might be interested in
Which of the binomials below is a factor of this trinomial?
adelina 88 [10]

Answer: Maybe its D not a 100% sure through.

Step-by-step explanation:

5 0
3 years ago
O
Volgvan

Answer:

Triangular prism?

Step-by-step explanation:

I done this riddle before but I dont remember to cleary of what the answer is.

7 0
2 years ago
The stem and leaf plot shows the number of items in each of the 12 collections in a museum.
Ivahew [28]

Answer:

2

Step-by-step explanation:

Khan acaremy

8 0
3 years ago
Solve x and y 3x-4y=18,9x-2y=12
Rudiy27

Answer:

3x-4y=18

1xy=18

xy=18 ans

4 0
3 years ago
Read 2 more answers
BRAINLIEST ANSWERS ONLY.
mars1129 [50]

Answer:

Heyy

Step-by-step explanation:

△ABC is a right angled triangle and right angle at B

sinA=

AC

BC

, cosA=

AC

AB

⟹sinA+cosA=

AC

BC

+

AC

AB

=

AC

BC+AB

[We know that sum of two sides of a triangle is greater than the third side]

⟹sinA+cosA>

AC

AC

=1

Hence, sinA+cosA>1

4 0
2 years ago
Other questions:
  • Z/-3 + 36 = 44 solve for z
    6·2 answers
  • In △ABC,a=13, b=14, and c=18. Find m∠A.
    14·2 answers
  • Write an equation to represent the following statement.<br> The product of 7 and j is 91
    6·1 answer
  • What is the answer to this
    10·1 answer
  • What is the correct verbal expression for the mathematical expression 5 - 2x?
    12·2 answers
  • how much carrots can a rabbit chuck chuck if a rabbit could chuck carrots Lol this is random but ill mark Brainliest if you put
    13·1 answer
  • A new restaurant has ordered 64 tables for its outdoor patio. if the manager arranges the tables in a square formation, how many
    15·1 answer
  • The equation of a curve is y = a^x
    15·1 answer
  • Solve for a<br> a +(-5) = -12<br> O a=-17<br> O a= -7<br> O a = 7<br> O a = 17
    8·2 answers
  • Points...............​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!