7 Deadly sin(s)
d/dx cos(x)
What is sin(x)?
This is the first step in performing U-Sub
What is choosing a U
The marginal cost of C(x) = 4x.
What is 4?
What concept finds minimums and maximums
What is the derivative?
The equation for the definition of a derivative
what is f'(x) = lim (h→0) [f(x + h) - f(x)] / h?
d/dx sin2(x)
What is sin(2x)?
Evaluate: ∫xex²dx
What is ½ex²+C
Revenue is price times this.
What is quantity?
This is the side length and height of an open-top box with volume 1000 cm³ that has the minimum surface area.
What is a square base of 10 cm and height of 10 cm?
d/dx x⁴.
What is 4x³?
The slope of y = sin(x) at x = 0.
What is 1
If u = 3x2, then du = ______
What is 6x dx
To maximize profit, set this function’s derivative equal to zero.
What is the profit function?
This is the x-coordinate at which f(x) = -x2+6x reaches its maximum.
What is (3, 9)?
d/dx ln(x).
What is 1/x
Evaluate: ∫cos(x) dx.
What is sin(x) + C?
Evaluate: ∫ln(x)2dx
What is xln(x)2-2xln(x)+2x+C
The change in the total cost that arises when the quantity produced is increased
What is marginal cost?
A farmer uses 120 meters of fencing to enclose a rectangular area along a river. These are the dimensions that give the maximum area.
What are 30 meters wide and 60 meters long?
d/dx (x² + 1)⁵.
What is 10x·(x² + 1)⁴?
Evaluate: ∫tan(x) dx.
What is -ln(|cos(x)|) + C?
Evaluate: ∫xln(x2+1)dx
What is ½(x2+1)ln(x2+1)-¼(x2+1)+C
Marginal Profit function.
What is R′(x) - C′(x)?
This is the set of dimensions that minimizes the surface area of a closed rectangular box with a square base, given that its volume is 108 cubic inches.
What is 3 x 3 x 12?
The result when you differentiate both sides of x² + y² = 25 with respect to x.
What is dy/dx = -x/y?