If `f(x)=x^3+b x^2+c x+d` and `0 le b^2 le c ,` then a)`f(x)` is a strictly increasing function b)f(x) has local maxima c)`f(x)` is a strictly decreasing function d)`f(x)` is bounded

Prove that the function f(x)=x^(2)+2 is strictly increasing in the interval (2,7) and strictly decreasing in the interval (-2, 0).

Let f: R->R be a differentiable function for all values of x and has the property that f(x)a n df^(prime)(x) has opposite signs for all value of xdot Then, (a) f(x) is an increasing function (b) f(x) is an decreasing function (c) f^2(x) is an decreasing function (d) |f(x)| is an increasing function

Prove that the function f(x)=(log)_e(x^2+1)-e^(-x)+1 is strictly increasing AAx in Rdot

Let f:[1,oo)->R and f(x)=x(int_1^xe^t/tdt)-e^x .Then (a) f(x) is an increasing function (b) lim_(x->oo)f(x)->oo (c) fprime(x) has a maxima at x=e (d) f(x) is a decreasing function

Prove that the function f(x)=x^(2)-2x-3 is strictly increasing in (2, infty)

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

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.

Prove that the following functions are strictly increasing: f(x)=log(1+x)-(2x)/(2+x)

The function f(x)=x/2+2/x has a local minimum at x=2 (b) x=-2 x=0 (d) x=1

Find the intervals in which the function f given by f(x) = 2x^(2) – 3x is (a) increasing (b) decreasing