AROC and Tangent Lines
Differentiability and Derivatives
Power Rule
Trig, ln(x), and e^x Rule
Quotient Rule
Product Rule
Easy (ALL WORTH 100 points)
100
The average rate of change of sqrt(x^3-4) over the interval [2,5].
What is 3?
100
Given s(x)=2x-6/x^2 . Explain the meaning of s'(3). Do NOT find s'(3).
What is
s'(3) is the slope of the line tangent to the graph of s at x=3?
OR
s'(3) is the instantaneous rate of change of the function s(x) at x=3?
100
Given g(x)=x^5-2x^2+e^pi . Find g'(x).
What is
g'(x)=5x^4-4x ?
100
The derivative of y=e^x AND z=lnx .
What is
y'=e^x
z'=1/x ?
100
Find the derivative of f(x)=2x^3cos(x) .
What is
f'(x)=6x^2cos(x)-2x^3sin(x) ?
100
A line that touches a curve at two points is called a(n) _________.
What is a secant line?
200
The equation of the tangent line for h(x)=2x-6x^2 at x=2.
What is
y=-22(x-2)-20 ?
200
The graph of k(x) is given about. Find all x values in the open interval (-1,10) where k(x) is not differentiable.
What is x=2, 5, 7 ?
200
Given f(x)=(3x-4)(2x+1) . Find f'(x).
What is
f'(x)=12x-5 ?
200
Find h'(x) .
What is
h'(x)=e^x+2/x^2+e ?
200
Let s(x)=f(x)sqrt(x) . Find s'(4).
What is 15?
200
The instantaneous rate of change of a function is its...
What is DERIVATIVE?!
300
The average rate of change of k(x) on the interval [-4,6].
What is
4/10 ?
300
Using the graph above, find g'(5), g''(5), g'(9), g''(-1), and g''(-2).
What is
g'(5)= 2
g''(5)= undefined
g'(9) = 0
g''(-1)= 0
g''(-2)= undefined ?
300
Given f(x)=sqrtx/4-4x+3/x . Find f'(x) (ensure your answer has non negative exponents).
What is
f'(x)=1/(8sqrtx)-4-3/x^2 ?
300
Find f'(x), given f(x)=ln(pi)+e^3-x^3 .
What is
f'(x)=-3x^2 ?
300
Find the derivative of y' when y=sinx/x^4 .
What is
y'=(xcosx-4sinx)/x^5 ?
300
Given k(x)=-1/x-3sin(x)-x^4 cos(x) . Find k'(x).
What is
k'(x)=1/x^2-3cos(x)-4x^3cos(x)+x^4sin(x) ?
300
A line of a slope of the curve at a particular point is called a(n) ________.
What is tangent line?
400
Order m'(6), k'(6), f'(6) from least to greatest.
What is k'(6), m'(6), f'(6)?
400
Given h(x)=sqrt(5)-2root(5)x+4x^3 Find h'(x). (ensure your answer has non negative integer exponents)
What is
2/(5root(5)(x^4))+12x^2 ?
400
Find d/dx cscx .
What is
-csc(x)cot(x)?
400
Let r(x)=f(x)/(k(x)) . Find r'(3) .
What is
-13/8 ?
400
Let g(x)=f(x)k(x). Find g'(7).
What is -2?
400
The buttons used on the calculator to estimate a derivative value.
What is math->8:nDerivative?
500
Let A(x)=2k(x)+3x . Which value(s) of x does the line tangent to the graph of A(x) have a slope of -5?
What is x=6?
500
Given h(x)=f(x)-3+2/x . Find h'(16).
What is
h'(x)= -4-2/16^2 ?
500
h(x)=sin(x)+3ln(x)+3x-f(x) . Find h'(4).
What is undefined?
500
Let L(x)=(k(x))/(k'(x)) . If L has a horizontal tangent line at x=1, find k''(1).
What is
k''(1)=-9/2 ?