If a function f(x)=(λ2−2λ−3)x4+(2λ+1)x3+21x+(8−λ) is monotonically increasing for all x∈R, then

Consider the function f: R→R defined by f(x)=sin(x)+cos(2x). Which of the following statements about f(x) is true?

If a function f(x)=(λ2−2λ−3)x4+(2λ+1)x3+21x+(8−λ) is monotonically increasing for all x∈R, then

If the function f(x) = kx3 - 9x2 + 9 x + 3 is monotonically increasing in every interval, then

Let f:→R→(0,∞) be strictly increasing function such that limx→∞f(7x)f(x)=1. Then, the value of limx→∞[f(5x)f(x)−1] is equal to

4. Determine whether x3 is O(g(x)) for each of these functions g(x).a) g(x) = x2 b) g(x) = x3 c) g(x) = x2 + x3d) g(x) = x2 + x4 e) g(x) = 3x f ) g(x) = x3/2