Find the relative extrema, if any, classify as absolute max/min.

a.) f(x)= x+1/x-2 on [2,4]

b.) f(x)= x^(2) -2x-3 on [-2,3]

c.) f(x)= x^(2/3) (x^2-4) on [-1,3]

Solve for x:

a.) 6^(2x) =36

b.) 2^(2x) -4 * 2^(x) +4=0

c.) 3^(x-x^2) =1/9x

Determine if the following statements are true or false. If it is true, explain why. If it is false, provide an example.

a.) If a and b are positive numbers, then (a+b)^x=a^x+b^x

b.) If x < y, then e^x < e^y

c.) If 0 < b <1 and x < y then b^x > b^y

d.) if e^kx > 1, then k > 0 and x >0

Find the volume of the solid generated by revolving the region bounded by y = sqrt(x) and the lines and y=2 and x=0 about:

1) the x-axis.
2) the y-axis.
3) the line y=2.
4) the line x=4.

Find the absolute maximum and absolute minimum values of the function, if they exist, on the indicated interval. 6) f(x) = x 4 - 32x 2 + 2; [-5, 5]

Evaluate (please answer all of them)

1) ∫ 1.67 ?^(1/3) ?? =

2) ∫ [(?^3+ sin(4?)) / (?^4−cos(4?)+4)] ?? =

3) ∫ ???^8(4?)cot(4?) ?? =

4) ∫ sec^2(4?) ???^5(4?) ?? =

5) ∫ (4x^3) / ((x^4)+3) dx=

Show that at every point on the curve

r(t) = <(e^(t)*cos(t)), (e^(t)*sin(t)), e^t>

the angle between the unit tangent vector and the z-axis is the same. Then show that the same result holds true for the unit normal and binormal vectors.

A rectangular box is to have a square base and a volume of 40 ft³. If the material for the base costs $0.35 per square foot, the material for the sides costs $0.05 per square foot, and the material for the top costs $0.15 per square foot, determine the dimensions of the box that can be constructed at minimum cost.

= Length

Width

Height

how do i find length width and height

Let f(x)=(x^2+1)*(2x-3)

Find the equation of the line tangent to the graph of f(x) at x=3.

Find the value(s) of x where the tangent line is horizontal.

4) A company manufactures and sells x lime scooters sets per month. The monthly cost and price-demand equations are

Cx=16,000+75x

p(x)=200-x/30 0≤x≤3,000

a) Find the maximum monthly revenue.

b) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each scooter.

c) If the local government decides to subsidize the company $5 for each scooter it produces, how many scooters should the company manufacture each month to maximize its profit under this revised scenario? What is the maximum profit? What should the company charge for each scooter?

What are the basic facts about?

a- Sums, differences, and products of power series?

b- Substitution of a function for x in a power series?

c- Term-by-term differentiation of power series?

d-Term-by-term integration of power series?

3) A company manufactures and sells x cellphones per week. The weekly cost and price-demand equations are

Cx=5,000+84x

p(x)=300-0.2x

a) What price should the company charge for the phones, and how many phones should be produced to maximize weekly revenue? What is the maximum revenue?

b) What is the maximum weekly profit? How much should the company charge for the phones, and how many phones should be produced to realize the maximum weekly profit?

Find the particular solution to the equation.

y''-4y'+5y=(e^(2t))(sec(t))

please explain simpson's rule and how i can use it for approximation

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds.

1) Let P(x) = 3x(x − 1)³ (3x + 4)² . List the zeros of P and their corresponding multiplicities.

2) Let f(x) = −18(x + 3)² (x − 2)³ (x + 71)⁵ . Describe the end behavior of f by filling in the blank below.

As x → −∞, f(x) → .

As x → ∞, f(x) → .

3) The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 3 and roots of multiplicity 1 at x = 0 and x = −2. It goes through the point (−3, 108). Find a formula for P(x).