Mathematics Homework Help

d[f(x)]n/dx= n[f(x)]n -1 f’(x) and df(x)/dt=(df(x)/dx)•(dx/dt)

Your company produces smart-phone covers and finds that its cost functions is C(x)=100 x1/2 +200. The marginal average cost is

50x-3/2 — 200x-2 .

The 1st derivative of the function f(x) = (x + x2)1/4 is (1/4)(x + x2) (-3/4) (1+2x).

d[f(x) g(x)]/dx= f’(x)/ g’(x)

The integral ʃx2 dx/(x2-1) can be evaluated using the substitution u=x2-1.

Suppose the rate of growth of bacteria in a Petri dish is given by q(t) = 42t, where t is given in hours and q(t) is given in thousands of bacteria per hour. If a culture starts with 20,000 bacteria, find a function Q(t) that gives the number of bacteria in the Petri dish at any time t.

d[af(x)]/dx=af(x) ln(a)

ʃ ef(x) f’(x)dx=ef(x( + c

The unit price p and the quantity demanded q of a certain product are related by the equation p = − 2q + 10. The elasticity of demand E(p) is:

A manufacturer determines that his total cost function is C(q)=4q3 – q + 1. Where q is the number of units produced. Find the level of output at which the average cost is minimized.

Given E(p) = p/(120 — 2p). At what price is the elasticity of demand equal to 1?