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# Inflection points from graphs of function & derivatives

AP.CALC:
FUN‑4 (EU)
,
FUN‑4.A (LO)
,
FUN‑4.A.10 (EK)
,
FUN‑4.A.11 (EK)
Identifying inflection points from graphs of function, first derivative and second derivative. Graphs are done using Desmos.com.

## Want to join the conversation?

• Could you say that if f''(x) is positive the slope is accelerating and if f''(x) is negative that the slope is decelerating and that is f''(x) = 0 then the slop is constant.
• Yes, the slope of f'(x) would be positive, meaning the slope of f(x) would be growing over time. Since f''(x) is acceleration vs time if f(x) is position vs time, the sign of f''(x) tells you whether f(x) is accelerating positively or negatively (it tells you the concavity).
• How did sal do that on desmos ?
• Why is Sal teasing us, not showing f(x)'s behavior when f''(x) bounces off the zero axis?!
(1 vote)
• f(x) just continues to increase; there's no change in direction (maximum/minimum) to make a curve because the f''(x) does not change sign