Derivatives and Tangent Lines
The derivative of 5x6-10x
What is 30x5-10
The behavior a graph has when f'(x)<0
What is decreasing?
The meaning of s'(t) and s''(t) if s(t) represents an object's position
What is velocity (s') and acceleration (s'')?
The number of different antiderivatives for a given function.
What is infinity?
The five towns that border Watertown.
What are Cambridge, Belmont, Newton, Boston, and Waltham?
The derivative of sin(x-4)+x1/6
What is cos(x-4)+1/6x-5/6
The behavior of the graph of f(x)=-x4-3x3+x at x=-3.
(increasing/decreasing/concave up/concave down)
What is increasing and concave down
The possible values of v(t) (the velocity of an object in m/s) if the object's speed is at least 6 m/s.
What is greater than or equal to 6 or less than or equal to -6?
The general antiderivative of f(x)=2x.
What is F(x)=x2+C.
The names of all 5 guidance counselors.
What is Ms. Orpen, Ms. Edwards, Ms. Monteiro, Mr. Surdam, Mr. Dowd?
The slope of the tangent line to the graph of y=3x2-8x+2 at x=1
What is -2?
What is f(x) is continuous at x=c, and the limit as x approaches c of f'(x) exists?
The velocity function of an object given the position function s(t)=\sqrt(x)
What is v(t)=1/2*x-1/2
The antiderivative of f(x)=5x2-1.
What is F(x)=5/3x3-x+C?
The three countries Ms. Telford has lived in.
What are the US, Canada, and Norway?
What is y-54=-36(x+3)
- f'(x)>0 for x>2
- f'(x)<0 for x<2
- f'(x) is not defined for x=2
answers may vary
The acceleration of an object at t=pi if its position is given by the function s(t)=3sin(x)
What is 0?
F(x) if f(x)=2sin(x-7)
What is F(x)=-2cos(x-7)+C?
The year Watertown was settled.
What is 1630?
The tangent line to the graph of y=25x-1 at x=5
What is y-5=-(x-5)?
Find the intervals of increase, decrease, concave up, and concave down for f(x)=x3-3x+8
What is:
- increasing: x<-1 and x>1
- decreasing: -1<x<1
- concave up: x>0
- concave down: x<0
Description of the motion of an object (moving forward/backward, speeding up/slowing down) whose velocity is governed by v(t)=-5t2+10t-4 at t=1.
What is moving forward and not changing speeed?
F(x) if f'(x)=4x+6.
What is 2/3x3+3x2+C?
The population of Watertown (to the nearest thousand).
What is 35,000 or 36,000?