K 12 A 12 C 8 1 7 1. Differentiate. DO NOT SIMPLIFY. [8K,1C] (a) y = 4" sin (5x) (b) y = (sin x + tan x )* (3x + 5) (C) y= 32x 2. Determine the slope of the tangent line to y = = at the point where x = = [4K]3. A tool shed, 250 cm high and 100 cm deep, is built against a wall. Find the shortest ladder that can reach from the ground, over the shed, to the wall behind. [6A] 4. A particle's distance (in meters) from a fixed point at time t (in seconds) is given by the function s (f) = e 'cost , 05/35. Find the time when the distance is at its maximum. [A4]5. Does the function /(x) = 2") have a horizontal tangent anywhere in its domain? Explain and justify your answer. [4C] 6. You are given g (x) = (4k -7)" for a positive constant k and g'(0)=2, determine the value of k. [2A,2C]7. If f (x) = 4f(x), then write a possible exponential expression for f (x) . Justify your answer. [2T] 8. At what value (s] of x on the graph f(x) = 2x 3" is the tangent horizontal? [5T,1C]