# Thread: Derivative and Graph shape questions

1. ## Derivative and Graph shape questions

I need help bad. I just can't seem to get these problems. Any help would be greatly appreciated.

1. a)Find the intervals on which f is increasing or decreasin
b)Find the local maximum and minimum values of f
c)Find the intervals of concavity and the inflection points

f(x)=(x^2) / ((x^2) + 3)

2.Find the limit using l'Hospital's rule where appropriate unless it's easier another way.

lim (as tapproaches 0) ((e^3t)-1) / t

3.^^^Same as 2^^^

lim (as x approaches infinity) (xe^(1/x)) - x

2. Originally Posted by Subby07
I need help bad. I just can't seem to get these problems. Any help would be greatly appreciated.

1. a)Find the intervals on which f is increasing or decreasin
b)Find the local maximum and minimum values of f
c)Find the intervals of concavity and the inflection points

f(x)=(x^2) / ((x^2) + 3)

2.Find the limit using l'Hospital's rule where appropriate unless it's easier another way.

lim (as tapproaches 0) ((e^3t)-1) / t

3.^^^Same as 2^^^

lim (as x approaches infinity) (xe^(1/x)) - x
for 2 by L'hospital's rule

$\displaystyle \lim_{t \to 0}\frac{e^{3t}-1}{t}=\lim_{t \to 0}\frac{3e^{3t}}{1}=3$

for 3

$\displaystyle \lim_{x \to \infty}x(e^{1/x}-1)=\frac{e^{1/x}-1}{1/x}$

The second is in the form for L.H 0/0

$\displaystyle \lim_{x \to \infty} \frac{e^{1/x}-1}{1/x}=\frac{\frac{-1}{x^2}e^{1/x}}{\frac{-1}{x^2}}=e^{1/x}=1$