Use differentials to approximate the change in R revenue= 50x-1.5x2 as sales increase from 13 to 15 dollars.

Q: Since the development of the iPod, the stock price of Apple has been growing rapidly and has been…

A: Given the development of the iPod that includes the stock price of Apple in which it grows rapidly…

Q: Find the derivative of the function. x² + 2 y = 2 – , - 2 -&x(x² + 2, y' = (2² – 2)4

A: Given: The function is, y=x2+2x2-27. The objective is to find the derivative of the function.

Q: obtain the second derivative of the function: y=2-5x^4+3/2x^2

A: Please refer the attached image for complete solution.

Q: Find the derivative of y = 2 + v2 + vx5 |2 + V2 + Vx5

A:

Q: 2. In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

A: Solution is given below:

Q: After 2 hours, the population of a culture of bacteria has increased by 50%. If the rate of growth…

A:

Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

A:

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

A: Let height of triangle = h Base = b Then, we are given that:

Q: Solve for the second derivative of f(x)=2x-2/x+5

A:

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: Given : θ = 26.75°

Q: Find the average rate of change of g(x) = 4x + 2 between the points (-3,-10) and (3,14)

A:

Q: Find the average rate of change of g(x) = - 4x³5 from = - - 3 to x = 1

A:

Q: 1.) y = (3x² – 1 ) (4x +7 )

A:

Q: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

A: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A:

Q: Find the derivative of the function. y = 5x² + 2* + 3

A: The sum rule of differentiation states that ddx(f(x)+g(x))=f'(x)+g'(x). The differentiation of the…

Q: If x + y represents a motorboat’s average velocity with the current, in miles per hour, its distance…

A: We can say Average Velocity=Average DisplacementTotal time=dt so according to the question…

Q: Assume that y varies directly with x. If y = -4.8 when x= -1.6, what is the constant of variation?

A: Given, y=-4.8 and x=-1.6 Suppose that constant of variation is k. We know that y varies directly…

Q: Two people start biking from the same point. One heads east at 13 mph, the other south at 17 mph.…

A: Given, two bikers start at same point. One heading east at 13mph and other heading south at 17 mph.

Q: solve for the first and second derivative of the function:

A: Given function is: f(x)=log2 cos x + ln π We need to find the first and second derivative of the…

Q: How would i calculate the instantaneous rate of change given at the given point (3,10.1)?

A: Let's find.

Q: x5/2+4 x3 y = 3

A: We have to find the derivative of the given expression: y=x52+4x3x3 Simplifying the given…

Q: What is the rate of change of the function y = - 2x – 1?

A: The rate of change

Q: Find the derivative of the function. y = 2  4√(9 − x2)

A: Given function: y=29-x24

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A:

Q: The volume of a cube is increasing at 24 cubic inches per minute. What is the rate of change of its…

A: volume of cube = side3 V= volume  x= side dVdt=24 in3/minutedxdt=? at x=2

Q: Explain why the derivative of x2 + y2 + 2 = 1 does not mean anything.

A: x2+y2+2=1 On simplification, we get ⇒x2+y2=1-2⇒x2+y2=-1 This curve does not exist as the sum of two…

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: Given that increasing altitude of the triangle dh=2cm/min The increasing area of the triangle dA =…

Q: Use differentials to approximate the change in profit corresponding to an increase in sales (or…

A: given function is                                            P=-0.1x3+200x-90;   x=60 now,…

Q: Assume the learning rate for new skills is proportional to the difference between the maximum…

A: The learning rate for new skills is proportional to the difference between the maximum potential for…

Q: Find the second derivative of y² + 2x³ = 1 – 4y

A: The given equation is y2+2x3=1-4y Rewrite as  y2+2x3+4y=1 differentiate…

Q: The growth rate of a culture of bacteria is proportional to the number of bacteria present and after…

A:

Q: Find the second derivative. y = 7x2 - V2 y" =

A: Given that y=7x2-x27 y=7x2-x217=7x2-x27 find the first derivative…

Q: Use differentials to approximate the change in the area of a square if the length of its side…

A: Area of a square with a side length of x cm is, Ax=x2 Here, x=5 cm & ∆x=5.32-5=0.32 cm Now…

Q: Computate the derivative Y= 9X V1-9x

A:

Q: The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the…

A: here we have

Q: A $1500 washing machine in a laundromat is depreciated for tax purposes at a rate of $125 per yeaar/…

A: It is given that a $1,500 washing machine in a laundromat is depreciated for tax purpose at a rate…

Q: Use differentials to approximate the change in profit corresponding to an increase in sales (or…

A:

Q: -y = a(10z² –8z+7)

A: Using composite derivative formula.

Q: Find the second derivative of y² + 2x³ =1– 4y

A:

Q: Find the derivative 3 y = 2 + Væ4

A: To find the derivative of the given function y=3x+x43 we use power rule of derivative. Power rule of…

Q: Find the derivative

A:

Q: Find the derivative. 4. y = 3x 6x - 7

A: Given  y=3x4+6x3+7 To take derivative , we apply power rule for each term  ddxan=nan-1 Derivative of…

Q: Calculate up to 3rd derivative the equation f(x) = 5x²(x+ 47)

A: We have to find the 1st,2nd,and 3rd derivative of the given function.

Q: Use differentials to approximate the change in the BMI when weight increases from 55 to 56.5 kg and…

A: Let's find.

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: Formula of area of triangle 12bhWhere b is the base and h is the altitude Chain rule (uv)'= u'v+uv'

Q: The intrest on an investment varies directly as the rate of intrest. If the intrest is $53 when thw…

A: Simplification of simple interest

Q: Determine the derivative. x – 2x + а) у- x+3 b) y = n(4x² – 5x)

A:

Q: The homicide rate decreases at a rate of 3%/yr in a city that had 800 homicides/yr in 2018. At this…

A: dH / dt = rate of change of homicide rate = - 3% = - 0.03 x HPlease see the white board for…