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:
As a decimal it can be written as 7.3 repeated
Answer:
Your heart rate would be 72 beats per minute
Step-by-step explanation:
You need to get 60 minutes so If you multiply 15 by 4, its 60. Do the same for 18 and your heart rate is 72 beats per minute
Answer:
-20.5
Step-by-step explanation:
Using a basic calculator, you divide 10.25 by -.5 which easily gives -20.5
Answer:
The tree is 12 feet tall
Step-by-step explanation:
Let a represent the length of where the bird was sitting to the oak tree
let b represent the height of the tree
let c represent the length at which the bird flew
by pythagoras theorem
c²=a²+b²
b²=c²-a²
subtitute in the values
