<p>Does anyone know where I can find an explanation of the relationship between f(x), the first derivative of f(x), and the sec derivative graphs. I keep getting these confused.</p>
<p>Can anyone clear this up for me? please?</p>
<p>If F'(x) is +positive, F(x) is increasing.
If F'(x) is -negative, F(x) is decreasing.</p>
<p>If F'(x) has a +pos to -neg sign change, it is a relative max.
If F'(x) has a -neg to +pos sign change, it is a relative min.</p>
<p>If F"(x) is +postivie, F(x) is concave up.
If F"(x) is -negative, F(x) is concave down.</p>
<p>If F"(x) changes sign, there is an inflection point.</p>
<p>F'(x) = first derivative of F(x)
F"(x) = second derivative of F(x)</p>
<p>max/min on graph of f(x)= zeros on graph of f'(x)
points of inflection of f(x)= zeros on graph of f''(x)= max/min of f'(x)</p>
<p>When you say "If F'(x) is +positive..." does that mean if f ' (x) if above the x-axis or if f '(x) has a positive slope? Or do they words "increasing/decreasing" refer to the slope of the graphs.</p>
<p>Sorry for all the questions, I am kinda slow at this. Everytime I think I understand, I do a practice problem and get all confused again.</p>
<p>It means F'(x) is above the x-axis. Positive y-values.</p>
<p>IS there a way to relate the f '(x) graph to the f " (x) graph.</p>
<p>Yes it is similar to the way you relate f(x) and f'(x). Here:</p>
<p>F''(x) -> +, F'(x) = increasing
F''(x) -> -, F'(x) = decreasing</p>
<p>well, it would be the same relationship between the graph of f(x) and f'(x). When f''(x)>0, f'(x) is increasing, and vice versa. When f '' (x) crosses teh x axis, there's a critical point at f ' (x)</p>
<p>thank you so much! I got so confused when I was trying to understand it by myself. I feel so much better now.</p>