Short Cuts
Using the Mean Value Theorem
Graphs
Tangent Lines
Other
100
What is the derivative of the function y= 3x^2 + √(x) ?
6x + 1
2√(x)
2√(x)
100
What does the Mean Value Theorem state (in terms of f(x))?
f'(c) = f(b) - f(a)
(b - a)
(b - a)
100
Of the three graphs shown, which one is f(x), f'(x), and f''(x)?
Blue is f(x), Red is f'(x), Green is f''(x)
100
Find an equation of the tangent line at x = 3 assuming f(3)=5 and f'(3)=2.
y = 2x - 1
100
In terms of limits, what is the derivative of f'(a)?
lim h-> 0 f(a + h) - f(a)
h
h
200
Find y' when y = arc sin (x/3)
1
3√[1-((x^2)/9)]
3√[1-((x^2)/9)]
200
What is f’c when f(x) = √(x) on the interval [9, 25] ?
f'c = (1/8)
200
Which graph is f(x), f'(x), and f''(x)?
Red is f(x) Blue is f'(x) Green is f''(x)
200
Find an equation of the tangent line to f(x) = √(x) at x=9.
y = (1/6)x - (1/2)
200
Calculate g'(x) where g(x) is the inverse of f(x) when f(x)= 7x + 6
1/7
300
Find the derivative of y = 5(x^2) cos (3x)
10x cos (3x) - 15(x^2)(sin 3x)
300
Find point(s) c when y = x^3 on the interval [-4,5]
c = +/- √(7)
300
The graph above shows f(x) on a closed interval. Which points show:
A) f'x = 0
B) f'x = undefined
C) f''x > 0
Note: You must get all parts right to get the points.
A) C, E, F
B) B, G
C) E
B) B, G
C) E
300
Find f(3) and f'(3) assuming the tangent line to y=f(x) at x=3 has an equation y=5x+2.
f(3) = 17
f'(3) = 5
f'(3) = 5
300
Find the second derivative of y = x - (4/x).
-8(x^-3)
400
Find y' when y = ln ((x^2)/(1-x)).
(2-x)
(x - x^2)
(x - x^2)
400
Find the coordinates of point c when y = x^(-1) between (2 , 1/2) and (8 , 1/8).
c = (4 , 1/4)
400
For what value of x is f(x) = x^(1/3) not differentiable?
x = 0
400
A particle starts at time t=0 (seconds) and moves along the x-axis so that its position (meters) at any time t>0 is given by f(t)=(t-1)^2 * (2t-3). Find the velocity of the particle at t=4. (include units!)
48 m/s
400
Using this chart solve for H'(3)= when H(x) = G(F(x)).
-16
500
FINAL JEOPARDY. All work must be shown! Each "point" awarded for your work translates to 100 points on Jeopardy.
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