topic here is calculus and vector

Hey to you, this work is posted to course hero because I have personal problem at home in Ukraine I need to attend too, I was given a go ahead to go but I was told to still do some things while I am at home which I believe is foolish because there is war going on and this is not for marks but a completion streak. reference for work is United state national guard reserve force combat medic program from last year in 2023.

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 and only question 5 have part a and b. I ask to do on paper as it is most easy to understand, please please please only do on paper

here is instruction below, again please do on paper otherwise I will not understand, I say this as I English not my first language and it will be best to see on paper

god bless you

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