# Help me with some calculus questions.. i couldn't go through..

• Jul 26th 2009, 07:04 PM
khai
Help me with some calculus questions.. i couldn't go through..
Help me with some calculus questions which I couldn't go through...

a) Find the intervals on which function is increasing and decreasing ?
f(x) = x^3 - 3x^2

b) Find the intervals on which function is increasing and decreasing ?
f(x) = 1 / x^2

c) what are critical numbers for:
i) f(x) = x^3 - 3x^2 and
ii) f(x) = 3x^4 - 4x^3

d) For which interval the function f(x) = 8x^3 - 2x^4 is concave downwards?

e) Find the points of inflection for f(x) = x^4 - x^3 ...
• Jul 26th 2009, 07:57 PM
pickslides
Quote:

Originally Posted by khai
Help me with some calculus questions which I couldn't go through...

a) Find the intervals on which function is increasing and decreasing ?

function is increasing on $\displaystyle \frac{dy}{dx}>0$

function is decreasing on $\displaystyle \frac{dy}{dx}<0$

that any help?
• Jul 26th 2009, 08:07 PM
McScruffy
Quote:

Originally Posted by khai
c) what are critical numbers for:
i) f(x) = x^3 - 3x^2 and
ii) f(x) = 3x^4 - 4x^3

Find the first derivative of your function, set the equal to zero and solve for x. Those are your critical points.

Quote:

d) For which interval the function f(x) = 8x^3 - 2x^4 is concave downwards?

e) Find the points of inflection for f(x) = x^4 - x^3 ...
The function is concave down when $\displaystyle f''(x)<0$ for all values of $\displaystyle x$ on a given interval. When the function changes concavity you have your inflection points.