14C - Conditions for differentiability
For the derivative to exist at the point \(x=a\), the following conditions must be satisfied:
- The gradient of the tangents on either side of the point \(x=a\) must converge to the same value.
- The graph/function must be continuous at the point \(x=a\).
- Points of discontinuity
- Asymptotes
- Endpoints of a domain
- Sharp points and cusps
14C - Example 1: Conditions for differentiability
For each of the following functions, write down the interval for which the derivative exists.
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14C - Example 1: Video solution
14C - Example 1: Practice
Question 1: If \(f(x)=\frac{-2}{(x+3)^2}-1\), write down the domain for the derivative function, \(f'(x)\). Question 2: If \(g(x)=\sqrt{5-2x}+2\), write down the domain for the derivative function, \(g'(x)\). 14C - Example 1: Solutions
Question 1: \(x\in (-\infty,-3) \cup (-3,\infty)\) Question 2: \(x\in(-\infty,\frac{5}{2})\) |