Calculus 1C — Applications of the Derivative
Part 3 of 3. Related rates, linear approximation, finding maxima & minima, optimization word problems, and Newton's method — the derivative earning its keep.
Now the payoff. The derivative isn't just abstract slope — it answers real questions: how fast is the shadow growing? what's the cheapest box? where is the maximum profit? This is part 3 of 3 of Calculus 1.
- 01 Related rates ELI5: two quantities are tied together by an equation; if one changes over time, the other is forced to change too. The trick: differentiate the relationship…
- 02 Linear approximation ELI5: near a point, a curve looks just like its tangent line — so use the easy line to estimate the hard curve: f(x) ≈ f(a) + f′(a)·(x − a). It's how you…
- 03 Maxima, minima & curve shape ELI5: a hilltop or a valley-bottom is flat for an instant — slope zero. So candidates for max/min are where f′(x) = 0. To tell which is which, look at the…
- 04 Optimization word problems ELI5: "what's the best?" problems — biggest area, cheapest box, shortest time. The recipe: write the quantity to optimize, use a constraint to…
- 05 Newton's method — how solvers find roots ELI5: to find where a function hits zero, stand at a guess, slide down its tangent line until you hit the x-axis, and use that landing spot as your next guess.…
next course: Calculus 2A — Integrals →