Module 4 Flashcards
1
Q
Def of critical number
A
If f’(c)= DNE or 0
2
Q
Mean value theorem
A
F’(c)= (f(b)-f(a))/(b-a)
3
Q
Rolled Theorem
A
- f(x) is continuous on [a,b]
- f(x) is differential on [a,b]
- f(a)=f(b)
Then there is a number c in [a,b] that f’(c)=0
4
Q
Local maximum
A
F’(x) goes from positive to negative
5
Q
Local minimum
A
F’(x) goes from negative to positive
6
Q
local minimum (2)
A
F’(x)=0 and f’’(x)>0
7
Q
Local maximum (2)
A
F’(x)=0 and f’’(x)<0
8
Q
Inflection points
A
F’(x) maxs and mins
9
Q
F(x) concave up
A
F’(x) is increasing or f’’(x) is positive
10
Q
F(x) concave down
A
F’(x) decreases or f’’(x) negative
11
Q
Intergal(x^n)dx
A
(X^n+1)/(n+1)+c
12
Q
Intergal(e^x)dx
A
E^x+c
13
Q
Intergal(a^x)dx
A
A^x/lna+c
14
Q
Intergal(1/x)dx
A
Ln|x|+c
15
Q
Intergal(1/(1+x^2))dx
A
Arctan(x)+c
16
Q
Intergal(1/sqrt(1-x^2))dx
A
Arcsin(x)+c
17
Q
Intergal(cosx)dx
A
Sinx+c
18
Q
Intergal(sinx)dx
A
-cosx+c
19
Q
Intergal(sec^2x)dx
A
Tanx+c
20
Q
Intergal(csc^2x)dx
A
Cotx+c
21
Q
Intergal(secx*tanx)dx
A
Secx+c
22
Q
Intergal(cscx*cotx)dx
A
-cscx+c
