Applications of derivatives

Related rates practice problems x^2 + y^2 = z^2 \;\Rightarrow\; 2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt} 10 related rates practice problems with answers and full solutions: balloons, ladders, cones, shadows, cars and angles, each with a clear setup. Optimization practice problems f'(x) = 0 \;\text{ or undefined} \;\Rightarrow\; \text{test critical points and endpoints} 10 calculus optimization practice problems with answers and full solutions: fences, boxes, cans, closest points, revenue and the fastest route. Curve sketching practice problems f'(x) > 0 \Rightarrow \text{increasing}, \qquad f''(x) > 0 \Rightarrow \text{concave up} 12 curve sketching practice problems with answers and full solutions: critical points, increasing and decreasing, extrema, concavity and asymptotes. Linear approximation practice problems L(x) = f(a) + f'(a)(x - a) 12 linear approximation practice problems with answers and full solutions: linearization, estimating roots and logs, differentials and error. Mean Value Theorem practice problems f'(c) = \frac{f(b) - f(a)}{b - a} 12 Mean Value Theorem practice problems with answers and full solutions: finding c, Rolle's theorem, checking hypotheses, bounds and counting roots.