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).
 
        
             
        
        
        
Answer:
8^2 = 64
unless you mean 8^2's square root then it is 8
Step-by-step explanation:
 
        
                    
             
        
        
        
Answer:
The expressions which equivalent to   are:
 are:
  ⇒ B
  ⇒ B
  ⇒ C
 ⇒ C
Step-by-step explanation:
Let us revise some rules of exponent
Now let us find the equivalent expressions of  
A.
∵ 4 = 2 × 2
∴ 4 =  
∴   =
 =   
 
- By using the second rule above multiply 2 and (n + 2)
∵ 2(n + 2) = 2n + 4
∴   =
 =   
  
B.
∵ 4 = 2 × 2
∴ 4 =  2²
∴   = 2² ×
 = 2² ×   
 
- By using the first rule rule add the exponents of 2
∵ 2 + n + 1 = n + 3
∴    =
 =   
 
 
C.
∵ 8 = 2 × 2 × 2
∴ 8 =  2³
∴   = 2³ ×
 = 2³ ×   
 
- By using the first rule rule add the exponents of 2
∵ 3 + n = n + 3
∴   =
 =   
 
D.
∵ 16 = 2 × 2 × 2 × 2
∴ 16 = 
∴   =
 =  ×
  ×   
 
- By using the first rule rule add the exponents of 2
∵ 4 + n = n + 4
∴   =
 =   
 
E.
 is in its simplest form
 is in its simplest form
The expressions which equivalent to   are:
 are:
  ⇒ B
  ⇒ B
  ⇒ C
 ⇒ C
 
        
             
        
        
        
Answer:
4
Step-by-step explanation:
 
        
             
        
        
        
Answer:
1 A the first store.
2. B The second store.
Step-by-step explanation:
1. The store with the dearest towel  is The First one ( $20 compared with $18).
2. The equation for the cost in the first store is P = 20n + 25. 
The cost in the second  store is given by P = 18n + 35.
For 15 towels first store charges:
20 * 15 + 25 = $325.
Second store charges:
18 * 15 + 35 =  $305.