hey guys, hope you can help me with this, heres the picture: 1. to find whether it is increasing or decreasing, f'(x)<0 is decreasing and f'(x)>0 is increasing. so first-> i took the derivative and got f'(x)=12x^2+60x-168 and set it to zero to find the critical numbers. I got x= -7 and x= 2. Next I plugged it back into the original to find where it is decreasing on the interval, f(-7)= 4(-7)^3+30(-7)^2-168(-7)+2 = 1276 f(2)= -182 now my question is what do i put in the blanks (the blanks with the decreasing and increasing interval) I can fill in one blank and that is local maximum at -7. 2. for A and B, i first took the f'(x) and got sqrt(x^2+4) + (x)(x / sqrt(x^2+4). Next, I took the second derivative and got f"(x)= 2x^2+x+4 / sqrt(x^2+4). I do not know what to do next. I keep getting confused about this interval stuff. Do i set it to zero? The point of inflection is when it changes from concave up to down and vice versa, so i find the critical numbers first? how do i get the point of inflection? For maximum and minimum, i need to find the critical numbers and plug it into the second derivative to see if they are greater, less, or equal to zero? I'll stop here and do the last problem tomorrow because i feel this is already too much. Hope I made it as clear as possible. Thanks for all the help !