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Grade Select GradeDifferential Calculus

Q. IF f ( x ) IS A DIFFERENTIABLE FUNCTION AND f ^’( x ) = log_1/3 ( log₃ ( sin x + a) ) , THEN FIND THE INTERVAL OF ‘’a’’ SO THAT f ( x ) IS DECREASING FOR ALL REAL VALUES OF x .

Bharat Makkar

11 Years agoGrade Select Grade

2 Answers

Jitender Singh

Approved Tutor Answer11 Years ago

Ans:
Hello Student,
Please find answer to your question below

If the f(x) is decreasing, then
$f'(x) < 0$
$log_{1/3}(log_{3}(sinx+a)) < 0$
$log_{1/3}(log_{3}(sinx+a)) < log_{1/3}1$
$log_{3}(sinx+a) > 1$
$log_{3}(sinx+a) > log_{3}3$
$sinx+a > 3$
$a > 3 - sinx$ ............(1)
Also for the domain of logarithm function,
$sinx + a > 0$
$a > -sinx$ …......(2)
Combining (1) and (2) we have
$a > 3-sinx$
Since x belong to R,
$a > 2$

Bharat Makkar

11 Years ago

but i think a > 4 as a =3 doesnt satisfy the equation.

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