example1-4

Consider the values of In 2 and In 3. In 2 = 0.693147 and In 3 = 1.098612 This leads to the following conclusion: Derivative of f(x) = b bh - 1 lim h = In b and if f(x) = b*, then f (x) = (In b) x by Example # 1: Determine the derivative of f(x) = 7* Example # 2: Determine the derivative of f(x) = (1.05)*-4 MCV4U Unit 5 - Activity 2 Example # 3: Find the equation of the line tangent to the curve f(x) = 2e* at x = In 3. Example # 4: A biologist is studying the increase in the population of a particular insect in a provincial park. The population triples every week. Assume the population continues to increase at this rate. Initially there are 100 insects. a) Determine the number of insects present after 4 weeks? b) How fast is the number of insects increasing when they are initially discovered? At the end of 4 weeks