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# Inflection points from graphs of function & derivatives

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?!
• 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
• I am learning Calculus BC right, cause a couple of times in the title of the videos it says AB.
(1 vote)
• Some of the topics from AB and BC overlap and might be covered in both courses on Khan Academy. So, a video from AB might reappear in BC if the topic is covered in both courses or if you are reviewing what you already learned in AB.
(1 vote)
• but at (0,2) the derivative is decreasing then it is increasing
(1 vote)
• Not quite. The derivative is strictly increasing there.

Observe the interval before (0,2). The derivative is negative but getting less negative and eventually becomes zero at the point. Now, observe the interval after (0,2). The derivative starts at 0 and slowly increases. So, see that the derivative is only increasing.
(1 vote)
• do the relative minimums and maximums of the second derivative have any significance?
(1 vote)
• Relative minima and maxima of the second derivative of a function can tell you where concavity changes (inflection points) in the first derivative, but it cannot tell you anything definite about the original function.
Even if the first derivative is known to have changes in concavity due to analyzing the second derivative, the properties of the function itself are primarily based on whether the first or second derivative is positive or negative, or the maxima and minima of the first derivative
(1 vote)
• g'(-1)=-1.75 I'm not sure what that means