The slope of the tangent to the curve y^3x + y^2x^2 = 6 at (2,1)

1 answer:

7 0

Y^3x + y^2x^2 = 6

Using implicit differentiation 

3 y^2.y'.x+y^3+2 y.y'.x^2+2 y^2.x=0

y'(3 y^2.x+2 y. x^2) = -y^3-2 y^2.x 

y' = -[y^2(y+2 x)]/[x y(3 y+2 x)] 

= -[y(y+2 x)]/[x(3 y+2 x)] 

Substituting x =2 and y = 1:

y' = -(1)(1+4)/[2(3+4)] 
 = -5/14 

The slope of the tangent of the curve at (2,1) will be:
m = -5/14

You might be interested in

3× at x = 2 evaluate the following

Nat2105 [25]

Answer:

the answer is 6.

Step-by-step explanation:

8 0

2 years ago

masons cell phone company charges $0.12 for every text message he sends plus $2.50 per month if mason sent 25 messages this mont

klemol [59]

Answer:

The answer would be $5.5

Step-by-step explanation:

First, multiply $0.12 by 25 to get $3. Add the $3 to $2.50 to get your answer of $5.5

3 0

3 years ago

Which equation is represented by the table? x y (x, y) 0 2 (0, 2) 1 –1 (1, –1) 2 –4 (2, –4) A. y = –2x B. y = x – 1 C. y = 2x D.

SashulF [63]

Answer: [D]: y = -3x + 2 .
__________________________________________________

4 0

3 years ago

Consider the equation 5 +x=n.

Marat540 [252]

Answer:

It's C.

Step-by-step explanation:

Any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be LESS than 5 only.

8 0

2 years ago

801,504 round to the nearest thousand

Gelneren [198K]

Answer:

802,000

Step-by-step explanation:

The number in the thousands place is 1, and the number to the right of it is 5. And if the number to the right is greater than or equal to 5 the place value that you are rounding goes up by one.

3 0

3 years ago