Statement 1: Both `sinxa n dcosx` are decreasing functions in `(pi/2,pi)` Statement 2: If a differentiable function decreases in an interval `(a , b),` then its derivative also decreases in `(a , b)` .

Consider the following statements in S and R S: Both sinx and cosx are decrerasing function in the interval (pi/2,pi) R: If a differentiable function decreases in an interval (a,b) , then its derivative also decrease in (a,b) .Which of the following it true? (a) Both S and R are wrong. (b) Both S and R are correct, but R is not the correct explanation of S. (c) S is correct and R is the correct explanation for S. (d) S is correct and R is wrong.

The function x^x decreases in the interval (0,e) (b) (0,1) (0,1/e) (d) none of these

Statement 1: Let f(x)=sin(cos x)in[0,pi/2]dot Then f(x) is decreasing in [0,pi/2] Statement 2: cosx is a decreasing function AAx in [0,pi/2]

Which of the following functions are decreasing on 0,(pi)/(2) ?

Statement 1: Both f(x)=2cos x+3sinxa n dg(x)=sin^(-1)x/(sqrt(13))-tan^(-1)3/2 are increasing in (0, pi /2) Statement 2: If f(x) is increasing, then its inverse is also increasing.

The function f(x) = x^(2) is decreasing in

Which of the following statement is always true? (a)If f(x) is increasing, then f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

Find the intervals in which the functions are strictly increasing or decreasing: x^(2) +2x-5

Find the intervals in which the functions are strictly increasing or decreasing: 6-9x-x^(2)

Statement 1: If both functions f(t)a n dg(t) are continuous on the closed interval [1,b], differentiable on the open interval (a,b) and g^(prime)(t) is not zero on that open interval, then there exists some c in (a , b) such that (f^(prime)(c))/(g^(prime)(c))=(f(b)-f(a))/(g(b)-g(a)) Statement 2: If f(t)a n dg(t) are continuou and differentiable in [a, b], then there exists some c in (a,b) such that f^(prime)(c)=(f(b)-f(a))/(b-a)a n dg^(prime)(c)(g(b)-g(a))/(b-a) from Lagranes mean value theorem.