Lecture 8: Instantaneous Rates and derivatives

Question 1

continuous functions

Answer 1

• let f and g be two continuous functions then:
• their sum f + g is continous
• their difference f-g is continous
• their product fg is continous
• their quotient f/g is continous for all x except when g(x) = 0
• their composition f * g is continous

Question 2

average rate of change

Answer 2

• find the average velocity for the time period
• changing the position/ change in the time

Question 3

rules of differentiation

Answer 3

• the derivative of any constant is zero
• for any exponent n, d/dx x^n = nm^n-1

Question 4

properties of derivatives

Answer 4

• for any constant c, d/dx(cf) = c X d/dx (f)
• for any two functions f and g, d/dx(f +g) = d/dx(f)+ d/dx(g)