Unit 1
What is a limit?
What is a limit is the y value a function approaches from both the left and the right side of a given x value.
What is power rule?
what is nxn-1.
What is chain rule?
what is f'(g(x)) x g'(x)
The number of gallons of water in a storage tank at time t, in minutes, is modeled by w(t). Interpret w'(10)=-8.
what is at 10 minutes, the amount of water is decreasing at a rate of 8 gallons per minute.
What is Mean Value Theorem?
What is if f is continuous [a,b] and differentiable on (a,b) then there exists a point c in (a,b) such f(c) = f(b)-f(a)/(b-a)
What is squeeze theorem?
What is a theorem that states if a function f(x) lies between two function g(x) and h(x) and the limits of each of g(x) and h(x) at a particular point are equal to L then the limit at that point is also equal to L.
What is the definition of the derivative?
What is this limit gives an expression that calculates the instantaneous rate of change (slope of the tangent line) of f(x) at any given x value.
Find the derivative of arctan?
What is 1/(x2+1)
Find the interval where f(x)=x3-12x+1 is increasing and decreasing.
What is decreasing (-2,2) because f'(x) < 0 and increasing on (-infinity,-2) and (2,infinity) because f'(x)>0
What is intermediate value theorem?
What is if f is continous (a,b) then f takes every value between f(a) and f(b).
What is the derivative of cos(x) - sin(x) + 5x2
What is -sinx - cosx + 10x.
Find the second derivative of f(x) = -3x3+4x-2 at f"(1)
what is 6.
Limit as x approaches 0 of 4x/ln(x+1)
Find the relative extrema where x3-12x+1 using the first derivative test.
Solve using Squeeze theorem, limit as x approaches 0.
x2 cos(1/x2)
What is 0.
Find the derivative of f(x)= 5x2-x
What is 10x-1
Solve y=1/(7x2-1)2
what is (-28x)/(7x2-1)3
The position, in meters, of a body at time t sec is s(t) is t3-6t2+9t. Find the body's acceleration each time the velocity is zero.
Using Mean Value Theorem, find where the instantaneous rate of change is equivalent to the average rate of change for y =x2-5x+2 on (-4,-2).
What is x=-3
Solve using IVT, (0,1), (3,5), (4,3),(8,7), (9,-1). On the interval 0<X<9 what is the minimum number of zeros?
What is 3.
Find the derivative of h(x) = (4x-1)/(3x+2)
what is 11/(3x+2)^2
Find the derivative of x3+y3=6xy.
What is dy/dx = (2y-x2)/(y2-2x)
At time t=4, the depth of snow is 28 centimeters. Use the line tangent to the graph of S at t=4 to approximate the depth of the snow at time t=6. Is the approximation an underestimate or an overestimate of the actual depth of snow at time t=6? Table: (0,1.8), (1,2.4), (4,2), (9,1.6), (12,1.3) of S'(t)
What is 32cm is an overestimate because s(t) is concave down.
Find the relative extrema of f(x)=5+3x2-x3 using the Second Derivative Test.
what is relative min at x=0 because f'(0)=0 and f''(0) > 0 and relative max at x=2 because f'(2) = 0 and f''(2) < 0