Differentiation

Concepts

• Derivative from Calculus 20 exercisesThe derivative of f at a is the limit of the difference quotient as h→0. It measures the instantaneous rate of change and is the…
• Rolle's theorem from Calculus 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 from Calculus 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…
• L'Hôpital's rule from Calculus 20 exercisesRule that computes limits of quotients in indeterminate form (0)/(0) or (∞)/(∞) by differentiating numerator and denominator sepa…
• Differentiability and continuity 10 exercisesIf a function f is differentiable at a point c, then f is continuous at c. The converse is false.