Answers to math 230

1. The dispose of a function at the point of its local or worldwide maxima is zero. Explain why victimization an example.The slope of a function is zero at the point of its local or global maxima because of the fact that it is the point where the function is horizontal, thus the slope is really zero. For example, given a function f(x) =-x2. The first derived function of f is -2x and equating it to zero will yield to solution x=0 which is our candidate for utmost or minimum point. Furthermore, we apply the second first derivative test. The second derivative is -2 thus 0 is a local maximum. Accidentally 0 is the only local maximum thus 0 is also the global maximum of the function. At x=0, f(x) =0, which has slope of 0.2. Show how the derivative of the function f(x) = (2x4) (3x+2)2 can be obtained with protrude using the product linguistic rule.We can differentiate the given function 2x4 (3x+2)2 without using the product rule by just simply distributing (2x4) to the term (3x+2) giving you 6x5+ 4x4. Afterwards, multiply it with the constant 2, thus you go 12x5+8x5. Now you can solve the derivative using the simple idea of getting the derivative of function. Hence you have (12)(5)(x5-1)+(8)(5)(x4-1) yielding you to 60x4+40x3 which is the derivative of the function f.3. Provide a sermon showing that the nail down of the function, f(x) =2x4 / (x-2) does not exist at x=2.It is possible that the limit of a given function doest not exist at a particular point. In the problem, to show that the limit of f(x) as x approaches 2 does not exist we need to get the right hand cheek and left hand side limit of f(x). The right hand side limit of f is corroborative infinity while the left hand side limit of f is negative infinity. Since they are not equal, we are forced to conclude that the limit of f(x) does not exist.ReferenceWhat the Derivative Tells Us About a Function. Retrieved October 12 2007 from http//www.ugrad.math.ubc.ca/coursedoc/math102/keshet.notes/chapter 5