hello, if you have seen a question like such before that is because it is me, I have asked similar question before for the completion streak, i will explain more in deatil becuase people have asked, I am in Kharkiv for past 1 month and will be here 1 more month, during this time I was in a course which is "United state national guard reserve force combat medic program" the module being calculs and vectors, I was given good to go back home to ukraine by cadre but was asked this which make no sense as its not marked, not graded not anything but need to be done correctly for completion streak which is why I am here now

if you take on this task, please do these on paper, there are 5 questions just it look like so much because image is big . I ask to do on paper as it is most easy to understand, please please please only do on paper

here is question below, in order from 1 to 5 thank you for understanding.

question 1

Suppose that f is a differentiable function with the derivative f'(x) = (x - 1)(x + 2)(x + 3). Determine the values of x for which the function f is increasing and the values of x for which the function is decreasing.Suppose that f is a differentiable function with the derivative f(x) = (x + 1)(x 2){x + 6). Find all the critical numbers of f, and determine whether each corresponds to a local maximum, a local minimum, or neither. \fDetermine the points of inflection for the following equation. Then conduct a test to determine the change of sign in the second derivative. 25 x2 + 483. Determine whether each function has vertical asymptotes. If it does, state the equations of the asymptotes. 5x - 4 3.r + 2 b. C. + 4r + 3 2 - or + 12 x - 6r + 9 4. Use the algorithm for curve sketching to sketch the following: a. - 9x3+ 15x + 30 f. f(x) - 4x 6x- - 2 b. f(x) = - 4x3 + 18x3+ 3 g. y