Finding x-intercepts and antiderivatives from slope and derivative conditions

[scorpa]

Hello Everyone,
I have been doing homework for two days straight and now I have hit a block and can't seem to get anything right. At the moment I am working on my last calculus unit- The Integral and have ground to a screeching halt I have a few questions that I was hoping someone could help me out with.

1) Determine the x-intercepts of the curve which has a slope of 2x+1 and passes through (1,-4)

2) If y' = o and y=1 when x=2 and y''-4=0, find the function

3) Find the antiderivative of x(3x^2-7)^-2dx

I just don't really know where to go with these. I am not looking for answers from all of you, I just need a boost to get me going, and explanations as to why you are doing it. My math book only gives examples and no explanations and I have to take the course by correspondance so I have no one else to help me out. Thanks for everything.

 

[dextercioby]

For the first,you're given the slope function.Find the function by integrating the slope.

For the second,you're given the second derivative,integrate twice and find the function.

For the third,think of some substitution that u could make.

Daniel.

 

[p53ud0 dr34m5]

1) you have [itex]\frac{dy}{dx}=2x+1[/tex]<br /> <br /> so, you set up the integral:<br /> $$\int dy = \int(2x+1)dx$$<br /> solve the indefinite integral, plug in for x and y, and solve for C.<br /> <br /> 3) this a u-sub problem, where $u=3x^2-7$ and $du=6xdx$<br /> <br /> 2) use the same concept as in #1[/itex]

 

[scorpa]

OK thanks for the help, I figured it out last night. My problem turned out that I wasn't reading the question quite right.