## curves

I'm doing calc review, and I've forgotten a lot of stuff. I hope someone could help out. I can do equations and numbers, but anything with graphs and shapes always confuses the heck out of me. Weird, but I'm a number guy, not a graph guy.

Chart:
X | 0 | 0<x<1 | 1 | 1<x<2 | 2 | 2<x<3 | 3 | 3<x<4 |
f(x) | -1 | neg | 0 | pos | 2 | pos | 0 | neg
F'(x) | 4 | pos | 0 | pos | dne| neg | -3 | neg
F"(x) | -2 | neg | 0 | pos | dne| neg | 0 | pos

let f be a function that is continuous on the interval [0,4). The function f is twice differentiable except at x=2. The function f and its derivatives have the properties indicted in the table above, where DNE indicates that the derivatives of f do not exist at x=2.

a) for 0<x<4, find all values of x at which f has a relative extremum. Determine whether f has a relative maximum or a relative minimum at each of these values. Justify your answer.

b.) On the axes provided, sketch the graph of a function that has all characteristics of f.

c.) let g be the function defined by g(x)=S(1 to x) f(t) dt on the open interval (0,4). For 0<x<4, find all values of x at which g has a relative extremum. Determine whether g has a relative maximum or a relative minimum at each of these values. Justify your answer.

d.)For the function g defined in part (c), find all values of x, for 0<x<4, at which the graph of g has a point inflection. Justify your answer.

Whatever notes I have, the function was always given. I cannot find a case where I have to create the function - it was always plug junk in. I understand how the positive and negatives work, but I don't understand the rest.

It's sad I can do inverse trig but I can't do a simple graph. ha

Thanks in advance for the help. It's highly appreciated.