What is the condition that f(x) = x³ + x² + kx has no local extremum?

If the function f(x) = x² - kx is monotonically increasing in the interval (1, ∞), then which one of the following is correct?

The tangent to the curve x² = y at (1, 1) makes an angle θ with the positive direction of x-axis. Which one of the following is correct?

Consider the following statements in respect of the function f(x) = sin x:

1. f(x) increases in the interval (0, π).

2. f(x) decreases in the interval $\left(\dfrac{5\pi}{2},3\pi\right).$

Which of the above statements is/are correct?