Great video, thank you. So basically, if youre quiz asks "what intervals is f(x) is conacave up/down" and they give you a graph of f'(x), just remember that when f'(x) has a negative slope, f(x) is concave down; when it is positive, then f(x) is concave up.
I would say be careful saying "decreasing" when you really mean negative. The first derivative test is based on negative and positives. The increasing and decreasing is related to the 2nd derivative. Other than that, good video.
Im confused on why you started in the negative y-axis for the last graph. Since the slope of y' is positive at the beginning shouldn't you start the graph on a positive y value instead of a negative one?
Actually, the derivative of sine x is cosine x , not -cosine x. you drew the graph correctly but stated it wrongly ......the derivative of cosine x is actually -sine x, but the verse is not true.
He stated it correctly. He drew the graph of -cos(x) given sin(x) because he was graphing the antiderivative, not the derivative. It's similar to thinking: "The derivative of ___ will produce sin(x)?" And the answer is -cos(x). He stated, quote: "The derivative of -cos(x) gives sine" and that is true.
kinda misleading. whether a function is increasing or decreasing has NOTHING to do with its position relative to the x axis. u determine if its increasing or decreasing by looking at the y values
the y of the derivative equals the slope of the original. so if the graph of the derivative below the x axis that means the slope of the original was negative, and same goes for when the derivative graph is above the x axis.
