Assignment 4 - Written component Math 100 - Fall 2024 Due: Friday, October 11 at 11:00 pm Please complete each problem on a separate piece of paper. You will need to scan your work and submit it electronically through Assign2. (1) Let f (2) = - V9 - x2 a) [10 pts] Find f'(x) using the definition of the derivative. No marks will be given if the definition is not used. b) [5 pts] Find equations of the tangent lines to the curve y = f(x) that are perpen- dicular to the line 9y + 8x = 3. (2) Consider the functions x - 2 Download x + 2 and h(x) = f(x . f(3 5m/ a) [8 pts] Find h'(4). b) [4 pts] Find an equation of the normal line to the graph y = h(x) at x = 4. (3) Consider the function x4/3 sin (22), if x * 0; f (20 ) = if x = 0. a) [7 pts] Find f'(0) or show that it does not exist.b) [9 pts] Does lim f'(x) exist? Is the function f'(x) continuous at x = 0? (Be sure to explain you answer.) (4) [15 pts] Let f(x) = x3e-3x Use mathematical induction to show that an f = (-1)n3ne -3x x3 - na2+ n(n - 1) n(n - 1)(n - 2) dan 3 27 for n > 1