Question

cton 23 Product and Quotlent Rules: Higher Order Dervatives Question 10 (of 11) 10.00 points 1 out of 3 attempts The manager of a company that produces graphing calculators determines that when x thousand calculators are produced, they will all be sold when the price is Assistance Check My Work 1,260 (x ) = dollars per calculator. View Hint 0.3x+15 At what rate is demand P(x) changing with respect to the level of production when 7,000 (x -7) calculators are produced? Round your answer to two decimal places Show Me Guided Solution Practice This Questio □□ dollars per thousand calculators Question Help Report a Probiem 名0 F2 FS 川1 F8 4.

Answer 1

Given,

$P(x) = \frac{1260}{0.3x^2 + 15}$

$\frac{\mathrm{d} }{\mathrm{d} x}P(x) = -\frac{1260}{(0.3x^2 + 15)^2} * (0.6x)= -\frac{756x}{(0.3x^2 + 15)^2}$

For x = 7 (7000 calculators)

$\frac{\mathrm{d} }{\mathrm{d} x}P(x=7) = -\frac{756*7}{(0.3* 7^2 + 15)^2} = -5.999388$

So, the demand change rate is -5.999388 dollars per calculator

= -5.999388 * 1000 dollars per thousand calculators

= -5999.39 dollars per thousand calculators