Interactive JEE Physics apex class Lab
Maxima & Minima: Visual Slope Explorer
Move the slider or tap the Peak/Valley buttons to see how Slope (dy/dx) = 0 works!
Coaster Height (y)
8.5 m
Physical Quantity
1st Derivative: Slope (dy/dx)
0.00 (FLAT!)
Zero at Peak & Valley
2nd Derivative: Curvature (d²y/dx²)
-1.6 (Frown ∩)
Negative = Maxima
⛰️ MAXIMA REACHED: Right at the hilltop, the tangent is completely FLAT (dy/dx = 0) and curvature d²y/dx² is NEGATIVE!
Ball Height (h)
20.0 m (MAX)
h = 20t – 5t²Velocity (dh/dt)
0 m/s (Stopped!)
dh/dt = 20 – 10tAcceleration (d²h/dt²)
-10 m/s² (-g)
Always Negative = Maxima
🏆 MAXIMUM HEIGHT: At t = 2s, upward velocity dh/dt = 20 – 10(2) = 0! Gravity (-10 m/s²) makes d²h/dt² negative!
Potential Energy (U)
3.0 J (MIN)
Lowest at BottomSlope (dU/dx = -Force)
0.0 (FLAT! Force = 0)
Equilibrium Point2nd Derivative (d²U/dx²)
+2.0 (Smile ∪)
Positive = Minima
💎 STABLE EQUILIBRIUM (Minima): At the bottom of the bowl, slope dU/dx = 0 and curvature d²U/dx² = +2 (Smile ∪)!
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