Use the Second Derivative Test to locate any relative extrema, if they exist. (Round your answers to two decimal places. If an answer does not exist, enter DNE.) f(x) = 1 3 x3 + 5 2 x2 + 6x − 5 relative maximum (x, y) = relative minimum (x, y) =

Here is a screenshot of the problem: https://gyazo.com/7c25d969fc2d85eeee2bbafe0cec23a3

The demand function for a certain item is

x=(p+2)9e−px=(p+2)9e−p

Use interval notation to indicate the range of prices corresponding to elastic, inelastic, and unitary

NOTE: When using interval notation in WeBWorK, remember that:
You use 'I' for ∞∞ and '-I' for −∞−∞.
And use 'U' for the union symbol.
a) The range of prices for elastic is

b) The range of prices for inelastic is

a) The prices for unitary is

3. Use the quotient rule for differentiation to find derivatives in each of the following:

(a) ?(?)=?²−?+1/?−1 (b) ?(?)=√?+2/2√? (c) ?(?)=?³+?²/?³−1

Why is the Fundamental Theorem of Calculus so important?
Give examples on how the method of substitution works with definite integrals.
What integrals lead to logarithms? Give some examples.

A company produces two types of solar panels per​ year: x thousand of type A and y thousand of type B. The revenue and cost​equations, in millions of​ dollars, for the year are given as follows. R(x,y)=4x+5y C(x,y)= x^2- 2xy+ 7y^2 +6x - 93y - 8

Determine how many of each type of solar panel should be produced per year to maximize profit.

Part 1-The company will achieve a maximum profit by selling ____ solar panels of type A and selling____solar panels of type B.

Part 2- The maximum Profit is $____million

7. Let A = (−1,3,0), B = (3,2,4) and C = (1,−1,5).
(a) Find an equation for the plane that passes through these three points.

(b) Find the area of the triangle determined by these three points.

8). Find an equation of the tangent plane to the surface z = x at (−4, 2, −1).

Calculus #3:

1.

a) Let A = (2,4,6),B = (1,2,3) and C = (5,5,5). Find point D so that ABCD is a parallelogram.

b). Two points X and Y are colinear if they lie on the same line. Are the points A = (3,6,−1), B = (2,0,3) and C = (−1, 3, −4) colinear? Justify your answer.

state and prove L'hopital's rule for the case of 0/0

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 6 sin(x) sin(y),     −π < x < π,     −π < y < π

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B1 is smaller than ∠B2.)

a = 77,    b = 104,    ∠A = 24°

Use the given transformation to evaluate the integral. (12x + 8y) dA R , where R is the parallelogram with vertices (−1, 3), (1, −3), (2, −2), and (0, 4) ; x = 1/ 4 (u + v), y = 1/ 4 (v − 3u)

Use ten steps in Euler’s method to determine an approximate solution for the differential equation y′ = x³, y(0) = 0, using a step size Δx = 0.1.

Using python boto3

Check if a folder is in an S3 bucket and if not in the bucket then it creates a folder in the right directory

A company estimates it will sell 5000 products in a year. It would like to make some number N of qually spaces orders of size x units per order so that the total inventory cost (which includes ordering and storage) is minimized.

a. If there is a $20 per order fixed cost plus a cost of $9 per unit ordered, and the storage cost per unit per year is $10, find the number of orders and the number of units per order that the goal of minimizing inverntory costs is achived.

b. Suppose that the ordering cost doubles to $18 per unit ordered, and that no other change is made. Decide whether this should or should not change the solution that you found in part a. , and justify your answer.

Use the derivative f' to determine the local minima and maxima of f and the intervals of increase and decrease. Sketch a possible graph of f (f is not unique).

f'(x)=30sin3x on [-4pi/3, 4pi/3]