`2f(x/2)+3f((2-x)/3)=g(x),0lt=x<3, f^(x)>0;` If `g(x)` is strictly increasing in `(a ,b)` and `g(x)` is strictly decreasing in `(c ,d)` then `25 a d-b c` is

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

The function f(x) = x^(2) - 2 x is strictly decreasing in the interval

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

If f(x)=x^3+b x^2+c x+d and 0

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

The real function f(x)=2x^3 - 3x^2 - 36x +7 is: a. Strictly increasing in (-infty,-2) and strictly decreasing in (-2,infty) b. Strictly decreasing in (-2,3) c. Strictly decreasing in (-infty,3) and strictly increasing in (3,infty) d. Strictly decreasing in (-infty,-2)U(3,infty)

The real function f(x)=2x^3 - 3x^2 - 36x +7 is: a. Strictly increasing in (-infty,-2) and strictly decreasing in (-2,infty) b. Strictly decreasing in (-2,3) c. Strictly decreasing in (-infty,3) and strictly increasing in (3,infty) d. Strictly decreasing in (-infty,-2)U(3,infty)

Find the interval in which f(x)=x^(3)-3x^(2)-9x+20 is strictly increasing or strictly decreasing.

Prove that the function f given by f(x)=logcosx is strictly increasing on (-pi//2,\ 0) and strictly decreasing on (0,\ pi//2) .

Let g(x)=2f(x/2)+f(2-x) and f''(x) < 0 AA x in (0,2). If g(x) increases in (a, b) and decreases in (c, d), then the value of a + b+c+d-2/3 is