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CBSE Class 12-science Answered

Find the intervals in which the function f(x) = sin^4x + cos^4x is increasing or decreasing where the range of x is ( 0, pie/2) .
Asked by Yogesh Misra | 01 Oct, 2018, 09:37: PM
answered-by-expert Expert Answer
f(x) = sin4 x + cos4 x
Find f'(x)  we get 
f'(x) = -2sin2x cos2x
f'(x) = -sin4x
As x is in the interval [0, ∏/2] hence 4x is in the interval [0, 2∏]
 
begin mathsize 16px style sin 4 straight x greater or equal than 0 space for space straight x element of open square brackets 0 comma straight pi over 4 close square brackets space and space sin 4 straight x greater or equal than 0 space for space straight x element of open square brackets 0 comma straight pi over 4 close square brackets sin 4 straight x less or equal than 0 space for space straight x element of open square brackets straight pi over 4 comma straight pi over 2 close square brackets space and space sin 4 straight x less or equal than 0 space for space straight x element of open square brackets straight pi over 4 comma straight pi over 2 close square brackets straight f apostrophe left parenthesis straight x right parenthesis less than 0 space for space 0 less than straight x less than straight pi over 4 straight f left parenthesis straight x right parenthesis space is space decre a s ing space on space open square brackets 0 comma straight pi over 4 close square brackets straight f apostrophe left parenthesis straight x right parenthesis greater than 0 space for space straight pi over 4 less than straight x less than straight pi over 2 straight f apostrophe left parenthesis straight x right parenthesis space is space increa s ing space on space open square brackets straight pi over 4 comma straight pi over 2 close square brackets end style
Answered by Sneha shidid | 03 Oct, 2018, 10:57: AM

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