Question

find the greatest and least value of (sin^-1 x)^2+(cos^-1x)^2

Answer 1

@ganeshie8

Answer 2

you'll get help if your face isn't that scary looking

Answer 3

f'(x)=0
x=tan1

Answer 4

just an observation : max value occurs when x=+-1

Answer 5

boundaries.

for min value we may have to differentiate. there seems to be no shortcut

Answer 6

but in exam we have to write n show ,evt,4 marker question..we just cant write observation based answers ;/

Answer 7

ok, set f'(x) = 0 and find the critical points

Answer 8

x=tan1

Answer 9

http://www.wolframalpha.com/input/?i=differentiate+%28arcsinx%29%5E2%2B%28arccosx%29%5E2+%3D0
so x=tan1

Answer 10

why do you set it =0?

Answer 11

after take derivative, set it =0 to get the critical points, but at the original input, you set the problem =0, why?

Answer 12

so if the curve is parallel to x axis somewhere we can know the point and then observe it from its LHL and RHL

Answer 13

i did it after taking derivative only

Answer 14

asin(x) = acos(x)
x = 1/sqrt(2)

Answer 15

http://www.wolframalpha.com/input/?i=differentiate+%28arcsinx%29%5E2%2B%28arccosx%29%5E2+
equate it to 0 now,same thing

Answer 16

thats ur oly critical point for the potential min/max

Answer 17

you need to check your function at below :-
1) x = 1/sqrt(2)
2) domain extremes (boundaries)

Answer 18

Max f = max{ f(1/sqrt(2), f(-1), f(1) }

Min f = min{ f(1/sqrt(2), f(-1), f(1) }

Answer 19

thanks!

Answer 20

np :)

Answer 21

one thing i wana point out

asin/acos is NOT atan

Answer 22

yes..:|