Question

If f(x)=ax^2+(x-b)^2 has critical point at (1,6) , determine if this critical point is maximum or minimum.

Answer 1

@ikram002p

Answer 2

http://www.wolframalpha.com/input/?i=minimum+or+maximum
Happy Studying!!!!!

Answer 3

@IAMTHEONE i know how to solve it but i'm not sure about my answer

Answer 4

@ikram002p i just want the values of a and b to compare it with my answer

Answer 5

ugh ok
i was typing it but somhow i get offline :|

Answer 6

ok can u solve it on a paper then just tell me what u did (explanation) and the answers
i mean summarized solution

Answer 7

or just give the answers and tell me the way u did it

Answer 8

ok

Answer 9

ok i got b=3,-2
and a=2,-3
did u got the same answer ?

Answer 10

f(1)=a+(1-b)^2=6
f'(1)=2a+2(1-b)=0

Answer 11

f''(x)=2a+2

Answer 12

yup i got the same thing here :) thanks alot

Answer 13

but why did u derive f(x) to the second derivative ?

Answer 14

but when I want to find if the critical point maximum or minimum I have to find the first derivative and I have two values for a and b so there will be two functions , right ?

Answer 15

second derivative
show u if its max or min
if f''(1)>0 min
if f''(1)<0 max
if f''(1)=0 faild
so i guess its depand u say
when b=3,a=2
then
f(1)=2*2+2=6>0 min
when b=-2,a=-3
then
f(1)=2*-3+2=-2<0 max

Answer 16

sry i made a typo last lines
f''(1)=6
f''(1)=-2

Answer 17

thanks I know that but It didn'r come to my mind lol

Answer 18

thanks a lot

Answer 19

oh ic ^^

Answer 20

np, ur wlc any time :)