be clear, exact & detailed. do not miss a step.

1. Calculus

Analyze the function. Find the intercepts, extrema, intervals of increase/decrease and concavity, points of inflection and make a sketch of the function , f(x) = (x-8)2/3

2. Vectors

An airplane is traveling S70W with a resultant ground speed of 414km/h . The nose of the plane is pointing west with an airspeed of 425km/h. Determine the speed and direction of the wind.

3. Calculus

Determine the constants a,b,c and d so that the curve defined by the cubic

f(x) = ax3+bx2+cx+d has a local max at the point (-2,4) and a point of inflection at the point (0,0)

4. Vectors

a) Determine the vector and parametric equations of the plane that passes through the points Q(-3/2 , 0 , 0) , R(0,-1,0) n. and S (0,0,3)

b) Determine if the point P(1,5,6) is a point on this plane