Chapter 4: Applications of the Derivative
The critical points of the function f(x) = x4 - 2x2 + 1
What is x=0 and x=+/-1?
The two parts of the Fundamental Theorem of Calculus
What are (integral a->b) f(x)dx = F(b) - F(a) and d/dx (integral a->x) f(t)dt = F(x)*(x)'?
Equation for finding the area between 2 curves
What is Area= (interval a->b) (f(x)-g(x))dx?
What is Spork?
Ms. Li's favorite vegetable
What is broccoli?
The local max/min of the function f(x) = x4 - 2x2 + 1
What is x=-1 and x=1 are local mins and 0 is a local max?
Evaluate the definite/integral (integral 0->2) x(x2+1)dx
What is 6?
Equation for finding the volume of the solid body/volume as the integral of cross-sectional area
What is Volume= (interval a->b) A(y)dy?
Princeton High School's database for grades, attendance, and schedule
What is PowerSchool?
Ms. Li's favorite holiday
What is Thanksgiving?
The given limit of lim (ex-1-x/x2) (use L'Hopital's rule when necessary)
x->0
What is 1/2?
Find the derivative: d/dx (interval 0->x) root(1+t4) dx
What is root(1+x^4)?
Equation for finding the average value of an integrable function f(x) on [a,b]
What is Average Value= 1/(b-a) (interval a->b) f(x)dx?
Ms. Li's hobby outside of her beloved Math
What is music/art "stuff" (in general)?
The given limit of lim (x+1/x2+4x+3) (use L'Hopital's rule when necessary) x->-1
What is 1/2?
Determine the position function if the velocity is v(t) = -32t+10 and the initial position is s(0)=2
What is s(t)=-16t^2+10t+2?
Equation for finding the volume of revolution (disk method)
What is Volume= (pi)(interval a->b) R^2 dx = (pi)(interval a->b) f(x)^2 dx?
What is 1898?
Ms. Li's comfort food
What is Velveeta Shells Mac 'n Cheese or Asian Cuisine (in general)?
Domain and zeros of the function f(x) = x/x-9
What is the domain is (-∞,9) (9,∞) and the zeros are x=0?
Evaluate the integral: (interval -1->2) 6x(x2-1)2 dx
What is 27?
Equation for finding the volume of revolution (washer method)
What is Volume= (pi)(interval a->b) (R(outer)^2 - R(inner)^2)dx = (pi)(interval a->b) (f(x)^2-g(x)^2) dx?
Princeton High School's ranking on the list of best public high schools in America
What is #75?
Ms. Li's boyfriend's name