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 equationA =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:[tex](a)\hspace{3}-79.61mi/h^2[/tex][tex](b)\hspace{3}-4.36mi/h^2[/tex]Step-by-step explanation:Let's rewrite the equation as:[tex]A=26.5*(x^{-0.45 })[/tex]Now, let's find its derivate:[tex]\frac{dA}{dx} =(-0.45)*(26.5)*x^{-0.45-1} =-11.925*x^{-1.45} =-\frac{11.925}{x^{1.45} }[/tex]Let's evaluate x=0.27 and x=2:[tex]\frac{dA}{dx} \left \{  {x=0.27}} \right. =-\frac{11.925}{0.27^{1.45} }  =-79.61mi/h^2[/tex][tex]\frac{dA}{dx} \left \{  {x=2}} \right. =-\frac{11.925}{2^{1.45} }  =-4.36mi/h^2[/tex]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.