Question

According to data from a General Motors study, the average speed of your trip A (in miles per hour) is related to the number of stops per mile you make on the trip x by the equation
A =26.5/x^0.45 .†

(a) Compute dA/dx for x = 0.27. (Round your answer to two decimal places.)
(b) Compute dA/dx for x = 2. (Round your answer to two decimal places.)

Answer 1

Answer:

$(a)\hspace{3}-79.61mi/h^2$

$(b)\hspace{3}-4.36mi/h^2$

Step-by-step explanation:

Let's rewrite the equation as:

$A=26.5*(x^{-0.45 })$

Now, let's find its derivate:

$\frac{dA}{dx} =(-0.45)*(26.5)*x^{-0.45-1} =-11.925*x^{-1.45} =-\frac{11.925}{x^{1.45} }$

Let's evaluate x=0.27 and x=2:

$\frac{dA}{dx} \left \{ {x=0.27}} \right. =-\frac{11.925}{0.27^{1.45} } =-79.61mi/h^2$

$\frac{dA}{dx} \left \{ {x=2}} \right. =-\frac{11.925}{2^{1.45} } =-4.36mi/h^2$

Keep in mind that when we derivate A(average speed) we find the average acceleration, thats why the result is given in mi/h^2, also it explains the minus sign, because for every stop you make on the trip you are decelerating.