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Calculus
A company must purchase at least 500 credits but no more than2000 credits, at a cost of $800 per credit. The company finds that when it purchases between 500 and 1000 carbon credits, it earns $1200 in revenue per credit. However, its per-credit revenue is reduced by 20 cents for each credit purchased in excess of 1000 credits
a) Define the profit function P(x) as revenue minus costs (measured in dollars), where x is the number of carbon credits purchased.
Show that P(x) =400x 500 < x < 1000 (lines under <)
600x - 0.2x^2 1000 < x < 2000 (line under second <)
b) Are there any values of x with 500 < x < 2000 for which the derivative P'(x) is not defined? If so, state what these values are.
a) Define the profit function P(x) as revenue minus costs (measured in dollars), where x is the number of carbon credits purchased.
Show that P(x) =400x 500 < x < 1000 (lines under <)
600x - 0.2x^2 1000 < x < 2000 (line under second <)
b) Are there any values of x with 500 < x < 2000 for which the derivative P'(x) is not defined? If so, state what these values are.
Calculus
consider the curve y=x2 (squared) - 2x + 1
a) sketch the curve over the range x = 0 to x=3
b) evaluate the area bounded by the curve and the x-axis between the limits x=0 and x=1
a) sketch the curve over the range x = 0 to x=3
b) evaluate the area bounded by the curve and the x-axis between the limits x=0 and x=1
Calculus
given the curve y= 1/3 x3 (cubed) - 9x - 7
a) evaluate dy/.dx
b)for what values of x is dy/dx = 0
c)hence, state the values of x at which the curve possesses stationary points. (note not required to evaluate corresponding y values)
d)determine the nature of the stationary points of the curve.
a) evaluate dy/.dx
b)for what values of x is dy/dx = 0
c)hence, state the values of x at which the curve possesses stationary points. (note not required to evaluate corresponding y values)
d)determine the nature of the stationary points of the curve.
Calculus
Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward and the inflection points.
f(x)= ln (x^2-8x+52)
f(x)= ln (x^2-8x+52)
Calculus
The size of a population grows according to the formula p(t)=1000^0.01t, where time is measured in months. What is the average of the population in the first five months?
Calculus
You are designing a rectangular poster to contain 48 in^2 of printing with a 3-in. margin at the top and bottom and a 1-in. margin at each side. What overall dimensions will minimize the amount of paper used?
Calculus
For what value of a is the following vector field irrotational:A ( ) ˆi ( 2) ˆj (1 ) kˆ 3 2 2 = axy − z + a − x + − a xz
Calculus
Use double integral to find the area of the region. The region enclosed by both of the cardioids r=1+cosθ and r=1-cosθ.
Calculus
Implicit Differentiation of the following:
1.) x sin (5x+4y)=y cos x
2.) dr/dtheta for (theta^(2/7) + r^(2/7))=6
3.) dr/dtheta for (tan(r theta)=1/3
1.) x sin (5x+4y)=y cos x
2.) dr/dtheta for (theta^(2/7) + r^(2/7))=6
3.) dr/dtheta for (tan(r theta)=1/3
Calculus
Implicit Differentiation of the following
1.) (3xy+7)^2=18y
2.) 4y^2=(3x-2)/(3x+2)
3.)x=sin y
4.) x+cot(xy)=1
5.) x^4+sin y=x^3y^5
1.) (3xy+7)^2=18y
2.) 4y^2=(3x-2)/(3x+2)
3.)x=sin y
4.) x+cot(xy)=1
5.) x^4+sin y=x^3y^5
