Determine the absolute extrema for the following function

Question

QUESTION 1: Find the derivative of sin²(x)

QUESTION 2: Determine the equation of the tangent to the curve f(x) = 4x³+ 2x² + 7 at x = 1

QUESTION 3: Determine the absolute extrema for the following function on the given interval

G(x) = 2x³ + 3x² - 12x + 4 on [0, 2]

QUESTION 4: Water is poured into a canonical container at the rate of 10 cm³/sec. The cone points directly down, and it has a height of 30 cm and a base radius of 10 cm. How fast is the water level rising when the water is 4 cm deep? Refer the diagram given below.

QUESTION 5: Find expression for dy/dx, if y⁴ + x⁵ - 7x² = 0.