2. (a) Over the interval {7: s R, 0 S x S 2 11:} , how much points on the graph of the function y = 85in x have a tangent line with slope (i) 0 and (ii) 1? Use diagram to help explain your answer. (b) How does the answer changes for x e R? Explain why?| 1. (a) We know the derivative of f(x) = ex but what if we want a different base? Explain. (b) Develop a function in the form of y = 6* + sinusoidal function (for 6 > 0) ? Find the first and second derivatives of the function. (c) What will happen if we replace 6 with e?5. A researcher 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 838 insects. a) Determine the number of insects present after 6 weeks. b) How fast is the number of insects increasing i) when are they initially discovered? ii) at the end of 6 weeks? 3. Determine the coordinates of all points at which the tangent to the curve 8 is horizontal. x 28x2-6x+1