# A Clarification: Sketching the Derivative

• Mar 2nd 2010, 06:29 PM
CuriousThought
A Clarification: Sketching the Derivative
http://img69.imageshack.us/img69/892/6hdyoh1.jpg

The graph (in black) is f(x). When asked to for the interval of increase/decrease, would it be correct to say that f(x) is increasing for all values of x? However, f(x) appears to plateau at 1.5<x<2.5. I know a point of inflection occurs at (2, f(2)).

If f(x) is increasing for all values of x, how would I begin to sketch the first derivative (I would need an equation since I cannot draw free-hand curves in the program I use)?

The pencil lines indicate a guess: The quadratic first derivative and linear second derivative.

Could anyone please provide clarification?
• Mar 3rd 2010, 02:02 PM
jameselmore91
Keep in mind that the derivative of a function is always one order of x lower than the function itself. To me, the function you posted resembles a cubic which is shifted left by 2 units and shifted up 5/2 units. Giving the function f(x) = (x-2)^3 + 5/2 and deriving that would give you something of the form 3(x-2)^2.

The derivative of a cubic is a quadratic and your graph should look something like the attachment.
• Mar 3rd 2010, 03:19 PM
CuriousThought
Quote:

Originally Posted by jameselmore91
Keep in mind that the derivative of a function is always one order of x lower than the function itself. To me, the function you posted resembles a cubic which is shifted left by 2 units and shifted up 5/2 units. Giving the function f(x) = (x-2)^3 + 5/2 and deriving that would give you something of the form 3(x-2)^2.

The derivative of a cubic is a quadratic and your graph should look something like the attachment.

Thank you for the clarification. (Itwasntme)(Happy)