Prove that, f(x) `=x+2+(x-2)e^(x)` is positive for all positive values of x.

Show that f(x) = (x-2)e^x + x + 2 is positive for all positive values of x.

If f(x) = (x-1)e^x + 1 , show that f(x) is positive for all positive values of x.

If f(x)=(x-1) e^(x)+1 , show that f(x) is positive for all positive values of x.

The value of K in order that f(x)=sinx-cosx-Kx+5 decreases for all positive real values of x given by

If ((x-5)(x^2-2x+1))/((x-7)(x^2+2x+3)) is positive for all real values of x, show that x has no value between 5 and 7.

Let a and b be real numbers such the the function f(x)={(-3ax^2-2,x is differentiable for all x inR . The positive value(s) of a is (are)

Suppose that f(x) isa quadratic expresson positive for all real xdot If g(x)=f(x)+f^(prime)(x)+f^(prime prime)(x), then for any real x

If f(x)=e^x(x-2)^2 then

If f(x)=e^(x)(x-2)^(2) then-

Find the range of values of a if f(x)=2e^x-a e^(-x)+(2a+1)x-3 is monotonically increasing for all values of xdot