In Exercises 33-38, use the Second Derivative Test to find the local extrema for the function. 33. y = 3x – x + 5 34. y = x - 80x + 100 35. y = x' + 3x? – 2 36. y = 3x - 25x + 60x + 20 37. у хе 38. y = xe

Q: The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled…

A: Given: Nx=0.03x2+0.315x+34.23x is no of years after 2000

Q: What are the the mean value theorem in application of derivatives?

A:

Q: 11) differentiate the function and find the slope of the tangent line at the given value F(x)=…

A:

Q: Sketch the x^2 And the derivative And integration

A:

Q: 3. Why first derivative is zero at local maximum and local minimum of function in an open interval?

A: Given, Why the first derivative is zero at the local maximum and a local minimum of function in an…

Q: Find the critical points of the function by using algebraic partial derivatives test. Rx, у) - -х2 -…

A:

Q: In Exercises 20–21, find a formula for the derivative using the power rule. Confirm it using…

A: NOTE: Refresh your page if you can't see any equations. . take derivative (using power rule)

Q: An orchard has an average yield of 36 bushels of apples/tree if the density is 22 trees/acre. For…

A: Let x be the additional number of trees to be planted to maximize the total yield.

Q: Explain your understanding of the connection between the derivative of a constant and the slope of…

A: We need to establish a relationship between the derivative of a constant and the slope of the…

Q: (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (х, у) %3D…

A: Given query is to find relative extrimas

Q: What are the maximum and minimum values in application of derivatives?

A: We have to define the maximum and minimum values in application of derivatives.

Q: Which defines as the process of finding the derivative of a function? *

A: Here, to tell which defines as the process of finding the derivative of a function.

Q: On [-8,0] the value of the first derivative of f(x)= x^2 is positive. True or False?

A: The given function is fx=2x2. Obtain the first derivative of the function as follows:…

Q: What is the derivative of the function y = (3x+1)^5 (x^4 - 10)^6 y’ =

A: y=3x+15x4-106

Q: ) Calculate the derivative of f1 (x) = 2x4 - 3x3 + 1/2x2 + 3. b) Study the sign of the derivative…

A:

Q: Calculate the derivative.

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Consider the function              f(x) = x^2 -x +1 / x^2+1 If you were asked to find all the…

A:

Q: 5 Calculate the second and the third derivative of y = 6x – y": y"

A:

Q: In Exercises 45–74, compute the derivative using derivative rules that have been introduced so far.

A: Given that y=z+1z-1=z+1z-112

Q: How can linear approximation be used to approximate the changein y = f(x) given a change in x?

A: Given;                 y=fx How can linear approximation be used to approximate the changein y=f(x)…

Q: Explain how to determine Partial derivatives for y-value ?

A: For a multi variable functions like f(x,y) To find its partial derivative for y value, treat x as a…

Q: Qa/ Explain the rule of maximum and minimum using Derivatives with an example?

A:

Q: ABANATUAN CITY B. Compute the derivative function f using the definition of the derivative. Show…

A: Using definition of derivatives.

Q: firm produces a monthly quantity of a product given by the production function P(x) = 2000√x, where…

A:

Q: 3 b) Determine the derivative of - from First Principle. (5)

A: The derivative from first principle is given below. Hope this helps!

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: We have two approaches to classifying critical points as local minima or maxima: the first…

A: To find the local minima and maxima we use both the first and second derivative test  for functions…

Q: Find the slope of a line tangent to the curve of the implicit function xy +3y-68 =0, at the point…

A:

Q: Explain the rule of maximum and minimum using Derivatives with an example?

A:

Q: Find the slope of the graph of the function at the given point. y = x-1 y 2.0아 1.5 5. 1.0 0.5 0.5…

A: For slope  of  the curve differentiate w.r.t.x   dydx=ddx1x=-1x2   dydx5/6,6/5=-1x25/6,6/5=m…

Q: ind the first derivative of the function: y = 4x - 2x3 + 5 (ii) Differentiate the following…

A:

Q: Use central difference method to estimate the 1and 2nd derivatives of the following function at x=3…

A:

Q: Determine the second derivative of 2x+ y-- 4 y 6.x (y + 2)--9(y+2) A B - 6x (y+ 2)-+ (y + 2) - 6x (y…

A:

Q: Find relative extrema not using the first derivative test   s(x)=x^4-2x^2

A: We will use the second derivative test. But the route to second derivative passes through the first…

Q: Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x)…

A: Find derivatives

Q: In Exercises 67–73, estimate derivatives using the symmetric difference quotient (SDQ), defined as…

A:

Q: Draw the function x = 2y- y2 by using the tools of derivatives? %3D

A:

Q: 2. Use an example to show how to use the First Derivative Test for critical points

A:

Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: calculate the derivative with respect to x of the other variable appearing in the equation. 18)…

A: Given: x+y12=1x+1y To Find:  To calculate the derivative with respect to 'x'.

Q: In Exercises 41 – 46, confirm your results with a graphing utility. 41. For the function f(x)= x³ +…

A: We have to solve

Q: Explain how to determine Partial derivatives for x-value ?

A: Partial derivatives :- Let z=fx,y be function of two independent variables x and y. If we keep y  as…

Q: determine maximums and minimums by the Second Derivative Test, we differentiate y"=72 / (2-8)3…

A: topic  - local maxima and minima

Q: y = x-12; (4,) Use the derivative feature of a graphing utility to confirm your results.

A: We will solve the following

Q: In Exercises 31–38, find the slope of the graph of the function at the indicated point. Use the…

A:

Q: Determine the second derivative of y = v5x² + 1 Determine the third derivative of y = (x² – 1) (2x3…

A: Second derivative of5x2+1 is  d2dx25x2+1

Q: Use implicit differentiation to calculate the value of derivative y' at the solution point (2, y) =…

A:

Q: The maximum rate of change of the function 1 ----> at the point (1,-2) happens in direction of and…

A:

Q: Compute the derivative of the function y using derivative rules. y = (13x4 +5 - 5)³ (Express numbers…

A: