What's the key thing to remember when "deriving the derivative"?

substitute what dy/dx is into your second derivative

f(x) = x2 - 2x. Use limits to find the derivative. What's the setup & answer?

((x + h)2 - 2(x + h) - (x2 - 2x))/h; 2x - 2

When does a Mean-Value Theorem problem become a Rolle's Theorem problem?

When the graph has a horizontal tangent

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Calculus Chap 2 Review fo u!

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From derivatives via limits to Dinner Rolle's Theorem -- we're gonna experience it all! Have fun(damentals) reviewing our holiday calculus season as we get ready for a test!

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Questions 20

Answers

1
When you find 'c's' from the MVT, you're finding where the _____ and _____ are parallel.
secant; tangent
tangent; cotangent
secant; cosecant
horizontal; vertical
2
Find the derivative: f(x) = x³/4 + 4/x³ (hint: get LCM at end!)
(3x4 - 48)/(4x4)
(3x8 - 48)/(4x4)
(3x6 - 48)/(4x4)
(3x2 - 48)/(4x4)
3
Find the slope of the secant between x = 6 and x = 11 for f(x) = 2/(√(x - 2))
-1/15
-4/15
-7/45
-1/9
4
If x(t) = -16t² - 32t + 1280, find the velocity at 2 sec and the accel at 3 sec
-96 ft/sec; -16 ft/sec2
-96 ft/sec; -32 ft/sec2
-64 ft/sec; -16ft/sec2
-64 ft/sec; -32 ft/sec2
5
What's the key thing to remember when "deriving the derivative"?
pull out constants while deriving
substitute what dy/dx is into your second derivative
d/dy both sides instead of d/dx
throw on a dy/dx when deriving twice!
6
Find the derivative of: y = (x² - 2x)/(x² + 3x)
5x2/(x2 + 3x)2
(4x3 + 3x2 - 12x)/(x2 + 3x)2
(5x2 - 12x)/(x2 + 3x)2
6x2/(x2 + 3x)2
7
Find the slope of the tangent at x = 3 for f(x) = 2/√(x - 2) w/o a calculator
∅
0
-1
1
8
Find the derivative of: f(x) = (3x³ - 2x² - x)/ √x
(15/2)x3/2 - 3√x + 1/(2√x)
(15/2)x5/2 - 3√x - 1/(2√x)
(15/2)x5/2 - 3√x + 1/(2√x)
(15/2)x3/2 - 3√x - 1/(2√x)
9
f(x) = x² - 2x. Use limits to find the derivative. What's the setup & answer?
((x + h)2 - 2(x + h) - (x2 - 2x))/h; 2x - 2
((x + h)2 - 2(x + h) -x2 - 2x)/h; 2x + h - 2
((x + h)2 + 2(x + h) -(x2 - 2x))/h; 2x + h - 2
((x + h)2 + 2(x + h) -(x2 - 2x))/h; 2x - 2
10
Find dy/dx for: xy² - 2xy = y
(y2 - y)/(1 - 2xy + x)
(y2 - 2y)/(1 - 2xy + 2x)
(y2 + y)/(1 - 2xy + x)
(y2 + 2y)/(1 - 2xy + 2x)
11
When does a Mean-Value Theorem problem become a Rolle's Theorem problem?
When you can't apply MVT (discontinuous or point of non-diff)
When we have a fire drill
When the graph has a vertical tangent
When the graph has a horizontal tangent
12
Find the equation of the tangent at (-2, -32) for f(x) = 3x³ - 2x²
y = 44x + 56
y = 44x - 120
y = 24x + 16
y = 24x - 80
13
Find the derivative of y = 3sec²x - 4csc²x
6secxtan2x + 8cscxcot2x
6secxtan2x - 8cscxcot2x
6sec2xtanx - 8csc2xcotx
6sec2xtanx + 8csc2xcotx
14
What word did we all use the most when learning the Chain Rule?
hone
follows
stuff
trig
15
What are the parallel slopes of the secant & tangent lines in #5?
sin(2/π)
2/π
.69
π/2
16
If x(t) = 4√t - 2t, find the time when velocity is 0
2 sec
1.5 sec
.5 sec
1 sec
17
Find the derivative: f(x) = cos(3x/(x - 2))
6/(x - 2)2sin(3x/(x - 2))
2/(x - 2)2sin(3x/(x - 2))
-2/(x - 2)2sin(3x/(x - 2))
-6/(x - 2)2sin(3x/(x - 2))
18
Find the slope of the tangent line at (2, 2√3) for the circle x² + y² = 16
√3/3
√3/2
-√3/2
-√3/3
19
Find 'c' or 'c's' guaranteed by the Mean-Value Theorem for Derivatives: f(x) = cosx - 2 [- π/2, 0]
-.69
Can't do, H!
-.64
-.77
20
Derive: f(x) = 3/(2x - 1)⁵
-15/(2x - 1)6
-30/(2x - 1)6
30/(2x - 1)6
15/(2x - 1)6

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