# Math Help - Graph sketch

1. ## Graph sketch

Given:

$f(0)=f(2)=0$
$f'(x) < 0$ if $x < 1$
$f'(1)=0$
$f'(x) > 0$ if $x > 1$
$f''(x) > 0$

How can I sketch a graph of the function $f$ given these characteristics? How would it look and how can I prove this?

2. Originally Posted by AMaccy
Given:

$f(0)=f(2)=0$
$f'(x) < 0$ if $x < 1$
$f'(1)=0$
$f'(x) > 0$ if $x > 1$
$f''(x) > 0$

How can I sketch a graph of the function $f$ given these characteristics? How would it look and how can I prove this?
the curve intersect the x-axis at two points (0,0) and (2,0) and you have f'(1) is a critical point because f'(1)=0
f is increasing in the interval x>1 $(1,\infty )$ and decreasing in the interval $(-\infty , 1)$ and the curve is concave up for all values of x

I think the curve is $x^2-2x$