NUMBER OF STRICTLY INCREASING OR STRICLTY DECREASING FUNCTION

Let f and g be two differentiable functions defined on an interval I such that f(x)>=0 and g(x)<= 0 for all x in I and f is strictly decreasing on I while g is strictly increasing on I then (A) the product function fg is strictly increasing on I (B) the product function fg is strictly decreasing on I (C) fog(x) is monotonically increasing on I (D) fog (x) is monotonically decreasing on I

If f(x)=x/sqrt(a^2+x^2)-((d-x))/sqrt(b^2+(d-x)^2) then (A) f(x) is strictly increasing (B) f(x) is strictly deceasing (C) f\'(x) is constant (D) f(x) is neither increasing nor decreasing

Find the interval in which the function f given by f(x)=x^(2)-2x+3 is (a) Strictly increasing (b) Strictly decreasing

Show that the function f(x) = log cos x is : (i) Strictly decreasing in ]0,pi/2[ (ii) Strictly increasing in ]pi/2, pi [

Find the intervals in which f(x)=4x^(3)-45x^(2)+168x-16 is (i) Strictly increasing (ii) Strictly decreasing

Let f: RvecR be differentiable and strictly increasing function throughout its domain. Statement 1: If |f(x)| is also strictly increasing function, then f(x)=0 has no real roots. Statement 2: When xvecooorvec-oo,f(x)vec0 , but cannot be equal to zero.

Number of chromosomes can increase or decrease due to

Statement-1 e^(pi) gt pi^( e) Statement -2 The function x^(1//x)( x gt 0) is strictly decreasing in [e ,oo)

Increasing and decreasing Functions

Show that the function f(x)=x^2 is neither strictly increasing nor strictly decreasing on R .