What are the best resources for calculus 1?

Okay, so the answer to the question below is : y= -2x^3+6x^2+7 (+7 being c). I'm not sure how c = +7

The gradient of a curve is given by dy/dx= -6x^2+12x. They coordinate of the maximum turning point is 1. Find the equation of the curve.

I've been so confused for the past 3 hours and would appreciate some help!!

Does anyone know of any books that will help me self teach Calculus 1? I sucked at trig, barely passed the course. I am retaking College Algebra. Basically I need to learn Calculus 1 before I take the college course. Also I have a TI-89 I just bought that I don't know how to use if that helps pick a book.

The question is- Find the one sided limit (if it exists). lim=-1+ 1/x+1 or limx=0- 1(1/1+x)

I understand how to find a limit, but really confused on how to find the one sided. Do I plug in the limit?

I am struggling to put x in terms of y for this problem, so I think there must be another way to solve it. How do I minimize the distance to the origin of the equation 3x^2 + 10xy + 3y^2 = 9

I'm going to be traveling for work and I need to take a Calculus 1 class this summer that doesn't have proctored exams. I am fine with any class under $2000.

Say person 1 has an average velocity of -5.5 Person 2 has an average velocity of -7 And person 3 has an average velocity of -8, Rank the people’s average velocity from least to greatest

The problem

I've tried IBP like five, six, seven times... It hasn't worked at all. I factored out the constant (7 in this one) and then separate (1/x) and (1/ln9x) into the two parts.

u = 1/ln9x and v'=1/x for me...

SOS, I've done this problem so many times now that my brain is probably half-fried but if I can finish it, I only have three more assigned problems for the summer. Thanks!

Edit: Added the link to the problem. Hope it works!

[(x-2)(x+4)]²

seems simple, but im getting different answers from deriv calculators. and and im brand new to this. an answer is great, but step by step would greatly appreciated.

also, if your up to it. derivative of f(x)= sin(cos2x)

I can do this function:

x=-6

f(x)= kx+8 x<-6 -9x+k x>=-6

    =-46/7

but for the life of me I cannot figure out this one:

x=1

  f(x)= (-8x^2+48x-40)/x-1        x<1

           -2x+k                             x>=1

I've been doing great with my online class, but I can't get what I'm doing wrong here. I know I must be right on top of finding the answer, but I just don't know how to do the problem when 'k' is only present in one function.....