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Calculus 1 ALL REVIEW Flashcards | StudBud
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Calculus 1 ALL REVIEW
Calculus 1 ALL REVIEW
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1
Derivatives; The generalizaed power rule states that d/dx (g (x)^n) = n(g (x))^n-1 * g'(x)
True
False
2
Increasing and Decreasing Functions
Increasing ( 3/2, ∞) Decreasing ( -∞, 3/2
Increasing ( 3/2,∞) Decreasing (- ∞, ∞)
Increasing ( 2, ∞) Decreasing ( -2, 2)
Decreasing ( - ∞, 2/3) Increasing ( 2/3, ∞)
3
Mean Value f'(c) = f(b) - f(a)/b - a
x = 12
x = -12
x = 6
x = -6
4
Optimization
x = 22.36, y = 22.36
x = -22.36, y = -22.36
5
Differencials Use y = x^2 ; dy = 2x dx with x = 6 and dx = .07;
\approx35.16
\approx36
\approx36.84
6
Intergration
e^{\pi}+c
-e^{\pi}+c
e^{\pi}
7
Derivative Graphs : What is the derivative of the red graph
Orange
Red
Green
Blue
8
Derivatives
5\left(3t-2\right)^4+3
4\left(3t-2\right)^5+c
9
Intergration; what is the fundamental theorem of Calculus
f'(x) = F(x)
F(x) = f(x)
F'(x) = f(x)
10
Extreme Values
∞, 0
Undefined, 0
0
0 , undefined
11
Derivative Graphs : Are turning points for the first derivative graph x intercepts for the orginal graph?
False
True
12
Derivatives; f(x) = 10x^3 + 7x^2 - 3,786 WHat is the Second derivative of the function
f'(x) = 30x^2 + 14x
f''(x) = 60x + 14
13
Related Rates
a) 8 cm^3/s b) .078 cm^3/s
a) 8 cm^3/s b) 7.8 cm^3/s
a) .08 cm^3/s b) .0078 cm^3/s
a) .8 cm^3/s b) .078 cm^3/s
14
Derivative graphs : The graph g'(x) is shown, on what intervals(s) is g(x) concave downwards
(-1.25, 1)U(3.25,∞)
(-2.74,0) U (0, 3.23) U (4.52, ∞)
( -∞, -1) U ( 1, 3)
(-2.74,0) U (0, 3.23) U (4.52, inf)
15
Intergration
-1
.5
1
-.5
