The number of bottles of shampoo that a store will?

The number of bottles of shampoo that a store will sell in a month at a price of p dollars per bottle is


N(p) = 550 divided by (p+4)


Find the rate of change of this quantity when the price is $ 4 per bottle.








a. increasing by 8.6 bottles





b. increasing by 34.375 bottles





c. decreasing by 34.375 bottles





d. decreasing by 8.6 botlesThe number of bottles of shampoo that a store will?
N(p) = 550 / (p + 4)





The rate of change of this quantity can be calculated from the derivative of the above equation.


The derivative of N(p) = N'(p)





Before we can use the quotient rule to calculate the derivative, we first must calculate the derivatives of the numerator and denominator of the equation above.


The derivative of 550 with respect to p is 0.


The derivative of (p + 4) with respect to p is (1 + 0) = 1





The quotient rule states:


derivative of A/B = [(A')(B) - (B')(A)] / B虏





N'(p) = [(0)(p + 4) - (1)(550)] / (p + 4)虏


N'(p) = [(0 - 550] / (p虏 + 4p + 4p + 16)


N'(p) = -550 / (p虏 + 8p + 16)





Now we can calculate the rate of change of this quantity when the price is $4 per bottle.


N'(4) = -550 / (4虏 + 8*4 + 16)


N'(4) = -550 / (16 + 32 + 16)


N'(4) = -550 / 64


N'(4) = -8.6 bottles


N'(4) = 8.6 decreasing because of the negative sign

makeup powder