SEE questions in images below

There are a number of problems here; some solutions, not in order, are as follows:
(5),(9) You are asked to find the derivative using the definition. Typically that means using the limit definition. For (5) if f(x)=9.5x^2-x+2.4 ==> f'(x)=19x-1 where the domain for both f and f' is all real numbers. ((-oo,oo) ) For (9) g(t)=5sqrt(t)=5t^(1/2) ==> g'(t)=5/(2sqrt(t)) where the domain of g is t>=0 and the domain of g' is t>0. (Notice the difference: in the derivative you are dividing by a power of t, so t cannot be zero.)
For (6) and (8) you are asked to find the points where the function is not differentiable. For (6) the points are x=0 (the function is undefined) and x=3 (there is a cusp). For (8), f is not differentiable at x=-1 (the function is not continuous there) or x=2 (there is a cusp).
For question (7), you are asked to identify the position, velocity, and acceleration functions. Note that the velocity is the derivative of the position function (giving the instantaneous rate of change of position), while the acceleration is the derivative of the velocity function. Here c is the position function (the particle slowly moves away from the original point, then moves away more rapidly, then slows the rate until it stays at nearly a constant distance). b is the velocity function, and a is the acceleration. (Note that when (a) is zero, we have a maximum velocity, and when (a) becomes negative, the velocity decreases toward zero.)
Questions 1-4 all play on the same theme—identifying aspects of a graph and the graph of the function's derivative. Remember that f'>0 indicates that the function is increasing; the higher the value of f' the faster the rate of increase. If f'=0 there is the possibility of a local maximum, local minimum, or an inflection point. If f'<0 the function is decreasing.
(1) I. Looking at the graph of f', we see that the function increases, achieves a maximum, decreases to a minimum, then increases to a maximum, and then decreases. This matches (d).
II. The function is increasing at a constant rate (linear), decreasing at a constant rate, and then increasing at a constant rate, which matches (b).
III. The function decreases to a minimum, then increases, which matches (c).
IV. The function decreases to a minimum, increases with an inflection point to a maximum, and then decreases, which matches (a).
Using the same technique:
(2) lower left
(3) upper left (note that upper right indicates f' fails to exist at x=0)
(4) upper right
http://mathworld.wolfram.com/Derivative.html

http://mathworld.wolfram.com/InflectionPoint.html