Understanding Derivatives and Slopes

Derivatives are literally just finding how fast something changes at any exact moment.

Think of driving a car - your speedometer shows your derivative, how fast your position changes right now.

The definition looks scary but it's genius. Take any function, push a tiny bit forward,

see how much it rises, divide by that tiny push, then make the push

infinitely small. That's your slope at that exact point. For f(x) equals x squared,

you get f'(x) equals 2x. At x equals 3, your slope is 6. At x equals negative

2, slope is negative 4. One formula gives you the steepness

everywhere on the curve. It's like having a universal slope detector for any