Home
Class 12
MATHS
Let f and g be two differentiable functi...

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

Promotional Banner

Similar Questions

Explore conceptually related problems

Let f and g be two differentiable functions on R such that f'(x)>0 and g′(x) g(f(x-1)) (b) f(g(x))>f(g(x+1)) (c) g(f(x+1))

Let f and g be real valued functions defined on interval (-1, 1) such that g'' (x) is continuous, g(0) ne 0, g'(0) = 0, g''(0) ne 0, and f(x) = g''(0) ne 0 , and f(x) g(x) sin x . Statement I lim_( x to 0) [g(x) cos x - g(0)] [cosec x] = f''(0) . and Statement II f'(0) = g(0).

Let f (x) and g (x) be two differentiable functions, defined as: f (x)=x ^(2) +xg'(1)+g'' (2) and g (x)= f (1) x^(2) +x f' (x)+ f''(x). The value of f (1) +g (-1) is:

Let f (x) and g (x) be two differentiable functions, defined as: f (x)=x ^(2) +xg'(1)+g'' (2) and g (x)= f (1) x^(2) +x f' (x)+ f''(x). The value of f (1) +g (-1) is:

Let f(x) and g(x) be two continuous functions defined from R rarr R, such that f(x_(1))>f(x_(2)) and g(x_(1)) f(g(3 alpha-4))

Let f and g be two differential functions such that f(x)=g'(1)sin x+(g''(2)-1)xg(x)=x^(2)-f'((pi)/(2))x+f''((-pi)/(2))

If f(x) and g(f) are two differentiable functions and g(x)!=0, then show trht (f(x))/(g(x)) is also differentiable (d)/(dx){(f(x))/(g(x))}=(g(x)(d)/(pi){f(x)}-g(x)(d)/(x){g(x)})/([g(x)]^(2))

Let f and g be two real values functions defined by f(x)= x + 1 and g(x) = 2x-3 . Find 1) f+g , 2) f-g , 3) f/g

f and g differentiable functions of x such that f(g(x))=x," If "g'(a)ne0" and "g(a)=b," then "f'(b)=

If f(x) and g(x) are two differentiable functions, show that f(x)g(x) is also differentiable such that (d)/(dx)[f(x)g(x)]=f(x)(d)/(dx){g(x)}+g(x)(d)/(dx){f(x)}