A number is increased by 20% and then decreased by 25%. Find the percentage change.

Explanation

Differentiation finds rate of change. If y = xⁿ, then dy/dx = nxⁿ⁻¹. For y = x³: dy/dx = 3x². This gives gradient of curve at any point. At x = 2: gradient = 3(2)² = 12.

Integration is reverse of differentiation. ∫xⁿdx = xⁿ⁺¹/(n+1) + c. Used to find areas under curves. Definite integral gives actual area between limits.

Applications: finding maximum/minimum (set derivative = 0), velocity/acceleration (derivatives of displacement), area/volume problems. Calculus is foundational for physics and engineering.