# Sketching graphs

• Mar 31st 2013, 11:04 PM
Wattsy
Sketching graphs
Just wondering if I could get a hand with sketching a graph where you aren't given the function. These are the details that are given -: f(0)=-1 f'(0)=0. f'(2)=0 f'(x) <0 for x <2. f'(x) >0 for 0<x<2. f'(x) <0 for x>2. Any help with finding critical points would be appreciated (Nod) cheers (Nod)
• Apr 20th 2013, 12:19 AM
Re: Sketching graphs
f'(0)=0 f(0) = -1,
The gradient at x=0 is zero.

f'(2)=0
at x=2, the gradient is zero.

f'(x)<0 for x<2.
The gradient is less than zero for any value strictly less than x=2.

f'(x)<0 for x>2
The gradient is less than zero for any value strictly greater than x=2.

f'(x)>0 for 0<x<2.
The gradient is greater than zero for any values between (0, 2).

This seems to be a very disjointed graph.
• Apr 20th 2013, 09:00 AM
Soroban
Re: Sketching graphs
Hello, Wattsy!

Quote:

Just wondering if I could get a hand with sketching a graph where you aren't given the function.

These are the details that are given:
. . $f(0) = \text{-}1\qquad f'(0) = 0 \qquad f'(2) = 0$
. . $f'(x) < 0\,\text{ for }x < 2 \qquad f'(x) > 0\,\text{ for }0 < x < 2 \qquad f'(x) < 0\,\text{ for }x > 2$

Any help with finding critical points would be appreciated.

$f(0) = \text{-}1$
. . The graph has y-intercept $(0,\text{-}1)$

$f'(0) = 0$
. . There is a horizontal tangent at $(0,\text{-}1)$

$f'(2) = 0$
. . There is a horizontal tangent at $\left(2,f(2)\right)$

$f'(x) < 0 \,\text{ for }x < 2$
. . The graph is decreasing on $(\text{-}\infty,2)$

$f'(x) > 0\,\text{ for }0 < x < 2$
. . The graph is increasing on $(0,2)$

$f'(x) < 0\,\text{ for }x > 2$
. . The graph is decreasing on $(2,\infty)$

The graph seems to be a cubic function . . .

Code:

              |     *        |               |               |               |              Q     *        |          - - o - -               |          *  :  *               |        *    :    *       *      |        *      :      *               |      *      : . . ---*------+------*--------+-------*---         *    |    *        2           * -1|  *                      - - o - -                    *               |P               |               |               |                        *               |
There is a relative minimum at $P(0,\text{-}1).$

There is a relative maximum at $Q\!:\:x = 2.$
But we don't know the y-value of point $Q.$