Average/Instantaneous Rate of Change
Tangent Lines
The Derivative
Differentiability and Continuity
10
What is the average rate of change on the interval [0,2]?
-5/2
10
Write the equation of a tangent line at the point (2,1) with a slope of 6.
y-1=6(x-2)
10
Find f'(3) given that
f'(x)=(-6x+4)/x^2
-14/9
10
List the 3 different graphical features that would cause a function to be non-differentiable.
Discontinuous, vertical tangent, corner/cusp
20
What is the average rate of change of the function below from x=2 to x=4?
f(x)=3x^2-6x+7
12
20
Write an equation of a tangent line of the function below at x=4, given the instantaneous rate of change.
f(x)=sqrt(2x+1)
IROC=1/sqrt(2x+1)
y-3=1/3(x-4)
20
Find f'(1) and explain the meaning given that
f'(x)=12/x+6x-2
f'(1)=16
At x=1 the slope of the tangent line is 16.
OR
At x=1 the instantaneous rate of change is 16.
20
Identify the values of x for which the function below is non-differentiable.
x=-3, -2, 2, 4
30
Find the average rate of change over the interval from [-3,0] given the graph below.
4/3
30
Write the equation of the line tangent to f(x) at x=0 given that f(0)=2 and the graph of f'(x) below.
y-2=3(x-0)
or
y=3x+2
30
f(x) represents how many feet you have walked in x minutes. Explain what f'(4)=320 means.
At 4 minutes, you are walking at a rate of 320 feet per minute.
30
Identify the values of x where the function below is continuous, but not differentiable.
x=-3, 0
40
Find the instantaneous rate of change of the function below at x=1.
f(x)=3x
3
40
Write the equation of a tangent line to f(x) at the point f(2)=-7, given the derivative of f(x) is
f'(x)=sqrt((3x^2+2x-1)/(x^3+7)
y+7=1(x-2)
40
Find the derivative of the function using the definition of the derivative.
f(x)=3x^2+8x-2
f'(x)=6x+8
40
Sketch a graph that has 3 places where it is non-differentiable.
Show me your graphs :)
50
Find the instantaneous rate of change of the function below at x=2.
f(x)=2x^2-4x+6
4
50
Write the equation of a tangent line to the function below at x=1.
f(x)=x^2+4
y-5=2(x-1)
50
Find the derivative of the function using the definition of the derivative.
f(x)=1/(x+3)
f'(x)=(-1)/(x+3)^2
50
Name one of the 19 basic functions that would be not differentiable at x=0.
sqrt(x), x^(1/3), x^(2/3), |x|, 1/x, 1/x^2, ln(x), [x], csc(x), cot(x)