show that the sum of the x- and y- intercepts of any tangent line to the curve sqrt(x) sqrt(y) = sqrt(c) is equal to c.

1 answer:

5 0

The answer is √x + √y = √c 
=> 1/(2√x) + 1/(2√y) dy/dx = 0 
=> dy/dx = - √y/√x 

Let (x', y') be any point on the curve 
=> equation of the tangent at that point is 
y - y' = - (√y'/√x') (x - x') 

x-intercept of this tangent is obtained by plugging y = 0 
=> 0 - y' = - (√y'/√x') (x - x') 
=> x = √(x'y') + x' 

y-intercept of the tangent is obtained by plugging x = 0 
=> y - y' = - (√y'/√x') (0 - x') 
=> y = y' + √(x'y') 

Sum of the x and y intercepts 
= √(x'y') + x' + y' + √(x'y') 
= (√x' + √y')^2 
= (√c)^2 (because (x', y') is on the curve => √x' + √y' = √c) 
= c. hope this helps :D

You might be interested in

A turtle swims 1 7/8 miles in 1/6 hour.

FrozenT [24]

Answer:

Speed of turtle = 11.25 miles/hour

Step-by-step explanation:

1 7/8 miles / 1/6 hour

= 15/8 / 1/6

= 15/8 * 6

= 11.25 miles/hour

3 0

3 years ago

Read 2 more answers

Find the range of the function y= 9x-2, where x>-2

RideAnS [48]

Answer:The given function is .Minimum or maximum value:At the extremum (maximum or minimum) value, the function will have zero slope. So, differentiate the given function once and equate it to zero to get the extremum point.dy/dx=0Now, check whether the point x=0 is corresponding to the maximum value or minimum value by differentiating the function twice,As for all value of x, so x=0 is the point corresponding to minima.Put x=0 in the given function to get the minimum value.Domain and range:The function defined for all the values of the independent variable, x.So, the domain is .The range of the function is the possible value of y.The minimum value, for x=0, is y=7.The maximum value, as .Hence the range of the function is .The value of x for which the function is increasing and decreasing:If the slope of the function is negative than the function is decreasing, soThen, from equation (i), the value of x for which dy/dx<0,18x<0Hence, the function is decreasing for .While if the slope of the function is positive than the function is increasing, soThen, from equation (i), the value of x for which dy/dx<0,18x>0Hence, the function is increasing for

Step-by-step explanation:hope this helps

8 0

3 years ago

Please help asap!! problem down below!

Airida [17]

Answer:

Step-by-step explanation:

b c

c d

d a

y esa ser la responsable respuesta

5 0

2 years ago

Read 2 more answers

Last month maria purchased a new cell phone for $500. the store manager told her that her cell phone would depreciate by 70% eve

Aleksandr-060686 [28]

We have been given that last month Maria purchased a new cell phone for $500. The store manager told her that her cell phone would depreciate by 70% every 6 months.

We know that an exponential function is in form $y=a\cdot (1-r)^x$ , where,