COGS109 HW1 Functions and Derivatives DUE 10 30 AM FRI OCT 8 September 30 2010 Type your answers in a text file called hw1calculus txt and upload that file to icogsci1 for later submission with bundle see wiki for details Use parentheses and the carat shift 6 to write your answers out For example to write p x2 y 2 you would type x 2 y 2 1 2 Helpful derivative rules are listed on the second page 1 For the function f x x2 3x 4 find a f 0 b f 2 c f x 2 Plot a graph using Matlab for the following function f x 2x 3 a Save this plot as hw1 jpg and upload it to icogsci1 b What is the slope of the line c Where does it cross the y axis 3 Find the derivatives of the following functions 4 3 a f x x p 2x b f x x 50 2 c f x e x 1 1 Derivative Rules In the following rules f and g are functions x is a variable and c is a condf dg stant f 0 and g 0 are shorthand for dx and dx respectively d dx c 0 d c c 1 dx x cx d x x dx e e d f f 0 dx e e f d 1 dx ln x x d x x dx c c ln c d dx sin x cos x d dx cos x sin x d 2 dx tan x sec x d 0 dx cf x c f x d 0 0 dx f x g x f x g x d 0 0 dx f x g x f x g x d 0 0 dx f x g x f x g x f x g x 0 0 f x g x f x g x d f x dx g x g2 d dx f g x f 0 g x g 0 x chain rule 2