1. Suppose the demand for a certain item is given by D(p)=−2 p 2 −4p+300 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiaacIcacaWGWbGaaiykaiabg2da9iabgkHiTiaaikdacaWGWbWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGinaiaadchacqGHRaWkcaaIZaGaaGimaiaaicdaaaa@434F@ , where p is the price per item in dollars.

a. Find the rate of change of demand with respect to price.

b. Find the rate of change of demand when the price per item is $10.

c. Is the demand increasing or decreasing when the price per item is $10?

Solution

2. A company that manufactures bicycles has determined that a new employee can assemble M(d)= 100 d 2 3 d 2 +10 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytaiaacIcacaWGKbGaaiykaiabg2da9maalaaabaGaaGymaiaaicdacaaIWaGaamizamaaCaaaleqabaGaaGOmaaaaaOqaaiaaiodacaWGKbWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGymaiaaicdaaaaaaa@4313@  bicycles per day after d days of on the job training.

a. Find the rate of change of the number of bicycles assembled with respect to time.

b. Find the rate of change of number bicycles assembled when an employee has 2 days of job training.

Solution