# Can someone help with these problems. They're easy

• Aug 18th 2009, 07:02 AM
Thomasheen
Can someone help with these problems. They're easy
Im kinda new to the calculus thing but these questions have been really annoying me.

1.) Find any vertical, horizontal and oblique asymptotes of the function f(x) = (x^2-3)/(x-1)

2.) Let f(x) = x^3 + x^2 - 6x. Find the zeroes and use calculus methods to find the local max, min and inflection points of f(x) and sketch the graph of f(x)

• Aug 18th 2009, 07:10 AM
mr fantastic
Quote:

Originally Posted by Thomasheen
Im kinda new to the calculus thing but these questions have been really annoying me.

1.) Find any vertical, horizontal and oblique asymptotes of the function f(x) = (x^2-3)/(x-1)

2.) Let f(x) = x^3 + x^2 - 6x. Find the zeroes and use calculus methods to find the local max, min and inflection points of f(x) and sketch the graph of f(x)

1.) Vertical asymptotes: Solve x - 1 = 0.
Oblique asymptote: Use polynomial long division to express $\displaystyle \frac{x^2-3}{x-1}$ in the form $\displaystyle ax + b + \frac{c}{x - 1}$. The oblique asymptote is $\displaystyle y = ax + b$.

2.) Zeroes: Solve $\displaystyle x^3 + x^2 - 6x = 0$. Hint: Factorise (there's a common factor ....)
Stationary points: Solve $\displaystyle f'(x) = 0$. Use the sign test to determine the nature of the stationary points.
Graph: The shape is a positive cubic. Add the information found above.

If you need more help, please post your working and state exactly where you're stuck.
• Aug 18th 2009, 07:14 AM
Thomasheen
Quote:

Originally Posted by mr fantastic
1.) Vertical asymptotes: Solve x - 1 = 0.
Oblique asymptote: Use polynomial long division to express $\displaystyle \frac{x^2-3}{x-1}$ in the form $\displaystyle ax + b + \frac{c}{x - 1}$. The oblique asymptote is $\displaystyle y = ax + b$.

2.) Zeroes: Solve $\displaystyle x^3 + x^2 - 6x = 0$. Hint: Factorise (there's a common factor ....)
Stationary points: Solve $\displaystyle f'(x) = 0$. Use the sign test to determine the nature of the stationary points.
Graph: The shape is a positive cubic. Add the information found above.

If you need more help, please post your working and state exactly where you're stuck.

Im stuck everywhere. My maths is rubbish and I dont understand the question. I've never really done this before. If you could explain it in a way I could understand I'll sell you my soul (within reason ;))
• Aug 18th 2009, 07:26 AM
mr fantastic
Quote:

Originally Posted by Thomasheen
Im stuck everywhere. My maths is rubbish and I dont understand the question. I've never really done this before. If you could explain it in a way I could understand I'll sell you my soul (within reason ;))

Sorry, but I've explained what you need to do. If none of this makes sense, then you need to get extensive help from your teacher (one of his/her jobs) because you have significant troubles and gaps that need extensive filling.