Applications of derivatives

Concepts

• Rolle's theorem 20 exercisesIf f is continuous on [a,b], differentiable on (a,b) and f(a)=f(b), there is at least one c∈(a,b) with f^prime(c)=0.
• Mean value theorem 20 exercisesIf f is continuous on [a,b] and differentiable on (a,b), there is a c∈(a,b) such that the slope of the tangent at c equals the sl…
• Critical points 10 exercisesA critical point of f is a number c in the domain where f^prime(c)=0 or f^prime(c) does not exist. Local maxima and minima of a f…
• Local maxima and minima 10 exercisesA local maximum of f at c is a value f(c) greater than or equal to the values of f on some neighborhood of c; a local minimum, le…
• Concavity and inflection points 10 exercisesIf f^primeprime>0 on an interval, the graph is concave up; if f^primeprime<0, concave down. An inflection point is where the conc…
• Optimization problems 10 exercisesAn optimization problem seeks the largest or smallest value of a quantity subject to constraints, expressed as a function of one…
• Related rates 10 exercisesIn a related rates problem several quantities change with time t and are linked by an equation. The equation is differentiated wi…
• L'Hôpital's rule 20 exercisesRule that computes limits of quotients in indeterminate form (0)/(0) or (∞)/(∞) by differentiating numerator and denominator sepa…