Find the first, second and third derivatives of the following total cost function w.r.t. Q: TC = Q3/8 -8Q2 +5Q/2 + 180

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

Find the slope of each of the following production functions, y = f (L), where y is output and L is labor. Graph the functions f(L) and the derivative functions f'(L). Give the economic significance of the sign of the slope of the derivative functions (i.e., whether the derivative is increasing or decreasing in L). а. y = 10L b. y = 8L3 C. y = 3Lª

Solve for the derivatives of the following function. 1. y = 4x3 -7x- 2. у %3 3 3. y = xVx 4. y = 3x? - 5x+2 5. y = -14x-10