9. Given the function: f(x)=3x²+5x-17

a. find the interval where the function is increasing and where it is decreasing.

b. Clearly state the critical number(s) of the function.

c. Find the relative extrema of the function( using 1st derivative test). answer should be in (x,y)

10. Given the function: x³ - x² + 52x - 17

a. determine the intervals where the graph of the given function is concave upward and where it is concave downward.

b. Find any inflection points. answer should be in (x,y) format.

A large tank holds 1000 L of water into which flows a brine solution with concentration of 1 kg / L at a rate of 6 L / min. The solution in the tank is kept well stirred and is flowing out of the tank at a rate of 5 L / min. Determine when the concentration of salt will reach 0.5 kg / L.

please explain your choice.

A rhombus is NOT a

1. polygon
2. parallelogram
3. trapezoid
4. quadrilateral

Consider the function f(x) =x/x^2+1

(a) Find all values ofxfor which f(x) is positive or negative. Discuss the behaviour of f(x) as x gets very large (in both the positive and negative direction).

(b) Draw a sign diagram clearly showing the values of x for which f(x) is increasing and decreasing. Hence find the critical points off(x) and determine their nature.

(c) Draw a sign diagram clearly showing the values of x for which f(x) is concave up and concave down. Hence identify any points of inflection off(x).

(d) Sketch the graph of f(x), clearly showing all the features identified above.

Find the flux of the vector field F = (3x + 1, 2xe^z , 3y^2 z + z^3 ) across the outward oriented faces of a cube without the front face at x = 2 and with vertices at (0,0,0), (2,0,0), (0,2,0) and (0,0,2).

How much money will be in a savings accounts after 5 years if $150 is initially deposited in the account, $150 is deposited each month in the account and interest is compounded continuously at 9% per year?

Solve for x using the quadratic formula. Be sure to check solution(s). 2x2-4x +1=0

Solve for x using the quadratic formula. Be sure to check solution(s). 3x2-2x+4=0

How many and what type of solutions will you have with 4x2-7x+11=0

2 Real solutions

2 complex solutions

1 real solution

2. A manufacturer of men’s shirts determines that her costs will be 500 dollars for overhead plus 9 dollars for each shirt made. Her accountant has estimated that her selling price s(x) should be determined by sx=30-0.2x where x is the number of shirts sold. Thus, the revenue function is the selling price of shirts times the number of shirts sold, i.e. Rx=x(30-0.2x) where x is the number of shirts
3. Give the formula for the profit function where x is the number of shirts.

b. How many shirts should be produced to maximize profit?

c. At what price will the shirts be sold to maximize profit?

d. What is her resulting profit?

Use the ε-δ definition of limits to prove that lim x3 −2x2 −2x−3 = −6. 3 markx→1

Hint: This question needs students have a thorough understanding of the proof by the ε-δdefinition as well as some good knowledge of what is learnt in Math187/188 and in high school, such as long division, factorization, inequality and algebraic manipulations.

End of questions.

Sketch the region bounded above the curve of y=(x^2) - 6, below y = x, and above y = -x. Then express the region's area as on iterated double integrals and evaluate the integral.

Let r : R->R³ be a path with constant speed, satisfying

r"(t) = (4 sin(2t))i + (-4 cos t)j + (4 cos(2t))k for all t belongs to R:

Find the curvature w.r.t. t of r. (Hint: cos(2t), sin(2t), and cos(t) are linearly independent. i.e. if c₁cos(2t) + c₂sin(2t)+
c₃cos(t) = 0 for all t belongs to R, then c₁ = c₂ = c₃ = 0.)

Find the equation of the tangent line to the circle (x+2)² +y+5)² =4 at point (-4,-5) (

Greg wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Greg has 650 feet of fencing, you can find the dimensions that maximize the area of the enclosure.

a) Let WW be the width of the enclosure (perpendicular to the barn) and let LL be the length of the enclosure (parallel to the barn). Write an function for the area AA of the enclosure in terms of WW. (HINT first write two equations with WW and LL and AA. Solve for LL in one equation and substitute for LL in the other).


A(W)=A(W)=    
b) What width WW would maximize the area?
ww =  ft
Round to nearest half foot c) What is the maximum area?
AA =  square feet
Round to nearest half foot

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Use cylindrical shells to find the volume of the solid generated by rotating the given region about the x-axis.

y=e^x, y=1, x=2

Brain weight B as a function of body weight W in fish has been modeled by the power function B = 0.007W^2/3, where B and W are measured in grams. A model for body weight as a function of body length L (measured in centimeters) is W = 0.12L^2.53. If, over 10 million years, the average length of a certain species of fish evolved from 13 cm to 21 cm at a constant rate, how fast was this species' brain growing when the average length was 18 cm? (Round your answer in g/yr to four significant figures.)