please help me with this. Math210 Precalculus

(a) There is only one function whose derivative is equal to itself: namely f(x) = e* An infinitely long polynomial P(x) is defined below: P(x ) = 1+=+ 1.2.3 1.2-3.4 Use the calculus we have learned in this class to show that P(x) = ex. (b) The name "critical number" (a.ka. "critical point") was chosen by mathematicians because they felt it represented something very important. Critical numbers are used in a myriad of applications of Calculus such as optimization, curve fitting, and astronomical anomalies (e.g., black holes). In one or two sentences give a clear and complete explanation of why critical numbers are important in Calculus. Note: although you may wish to give the definition of a critical number and/or an example, points for this problem are awarded for effectively explaining why critical numbers are important in Calculus