Question

given f(x)=2(x+1)^2+3. Find the greatest value of 1/f(x)

Answer 1

1/3

Answer 2

how to do that?? why not 3??

Answer 3

as the smallest value of f(x) is 3, the greatest value of 1/f(x) is 1/3

Answer 4

the least value inside the square is zero so the least value of f(x)= 2* 0+3= 3,

Answer 5

my idea is:
g(x) = 1/f(x)
then g'(x) = -f'(x)/(f(x))^2

Answer 6

saruz's method is much easier =D

Answer 7

thx

Answer 8

see u r trying to find out the maximum value of \[\frac{1}{f(x)}\]so the minimum value of f(x) will give u the maximum vaue for the \[\frac{1}{f(x)} = \frac{1}{2(-1 + 1)^2 + 3} = \frac{1}{(2 \times 0) + 3} = \frac{1}{3}\]