Math 1F03 : Derivative of an Odd Function is an Even Function - Mathematics Assignment Help

Assignment Task :

Question 1: Recall that a function f is even if f(-x) = f(x), and odd if f(-x) = -f(x). 

(a) Using the chain rule, show that the derivative of an odd function is an even function. 

(b) Using first principles (and a change of variables), show that the derivative of an even function is an odd function. 

Question 2: A spotlight on the ground shines on the wall 12m away. If a man 2m tall walks from the spotlight toward the building at a speed of 1.6m/s, how fast is the length of his shadow on the building decreasing when he is 4m from the building? 

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