memory check 6

Fermat’s theorem

if 1) f has a local max or min at c and 2) if f’(c ) exists then f’ (c )= 0

Extreme value theorem

if f is continuous on a closed interval [a,b] then f has an absolute max and absolute min value

rolle’s theorem

if 1) f is continuous on [a,b] and 2) f is differentiable on (a,b) and 3) f(a)=f(b) then there is a number c in (a,b) such that f’(c )=0

Mean value theorem

if 1) f is continuous on [a,b] and 2) f is differentiable on (a,b) then there exists a number c in (a,b) such that f’( c)= (f(b)-f(a))/b-a or f(b)-f(a)=f’(c )(b-a)

newtons method

x(n)-f(xn)/f’(xn)