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What does a derivative actually look like? 📈 Watch how a secant line turns into the tangent line as two points on a curve get infinitely close. At exactly point a, the line kisses the curve at just one single point, perfectly capturing the function's instantaneous rate of change. Math is beautiful when you can see it! ✨ #Calculus #MathAnimation #Derivative #VisualMath
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The joke is that in calculus, the first derivative tells you whether a function is increasing or decreasing, while the second derivative tells you whether the first derivative is increasing or decreasing, so a positive second derivative only means the slope is becoming more positive over time, not that the slope is already positive. For example, a function can have a negative first derivative and a positive second derivative at the same time, meaning it’s still decreasing but beginning to turn a
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