Math Exam 2

Front 1

Give the definition of an inverse function g(x) of a function f(x)

Back 1

Let f(x) have a domain D and range R. If there is a function g(x) with domain R such that g(f(x))=x for xED and f(g(x))= x for ER then f(x) is said to be invertible. the function g(x) is calle the inverse function and is denoted f^-1(x). THe inverse of f(x) denoted (f^-1(x), is the function that reverses the effect of f(x)

Front 2

Des every function have an inverse function

Back 2

No. f(x)=x^2 does not have an inverse because it is not one to one

Front 3

what is marginal cost and why is it reasonable to use a derivative to estimate it

Back 3

marginal cost is the cost of producing another unit. = (x+1) - c(x). the derivative is the instantaneous rate of change, marginal cos tis the difference in cost of adding and additional unit

Front 4

(fg)'

Back 4

f'g+fg'

Front 5

(cf)'

Back 5

cf'

Front 6

(f/g)'

Back 6

gf'-fg'/g^2

Front 7

inverse fo f(x)

Back 7

g'(x)=1/f'(g(x))

Front 8

(f(g(x))'

Back 8

f'(g(x))*g'(x)

Front 9

(sinx)'

Back 9

cosx

Front 10

(cosx)'

Back 10

-sinx

Front 11

(tanx)'

Back 11

sec^2x

Front 12

(secx)'

Back 12

secxtanx

Front 13

(csc)'

Back 13

-cosxcotx

Front 14

(cotx)'

Back 14

-cos^2x

Front 15

(sin^-1(x))'

Back 15

1/sqrt(1-x^2)

Front 16

(cos^-1(x))'

Back 16

-1/sqrt(1-x^2)

Front 17

(tan^-1(x))'

Back 17

1/1+x^2

Front 18

(cot^-1(x))'

Back 18

-1/1+x^2

Front 19

(sec^-1(x))'

Back 19

1/abs(x)sprt(x^2-1)

Front 20

(csc^-1(x))'

Back 20

-1/abs(x)sprt(x^2-1)

Front 21

(e^x)'

Back 21

e^x

Front 22

(ln(x))'

Back 22

1/x

Front 23

(b^x)'

Back 23

ln(b)*b^x

Front 24

(logbx)'

Back 24

1/ln(b)*(x)'/x