Applications of Derivatives formula sheet

15 rows · CalcRef · sample of the first 6 rows

Applications of Derivatives
Formula	Statement	Conditions
Tangent Line	$y - f(a) = f'(a)(x - a)$	no restriction stated
Normal Line	$y - f(a) = -\frac{1}{f'(a)}(x - a)$	f'(a) ≠ 0.
Critical Points	$f'(c) = 0 \text{ or } f'(c) \text{ DNE} \Rightarrow c \text{ is a critical point}$	no restriction stated
First Derivative Test	$f' \text{ changes } + \to - \Rightarrow \text{local max}; \quad f' \text{ changes } - \to + \Rightarrow \text{local min}$	no restriction stated
Second Derivative Test	$f'(c) = 0: \quad f''(c) > 0 \Rightarrow \text{local min}; \quad f''(c) < 0 \Rightarrow \text{local max}$	no restriction stated
Concavity	$f''(x) > 0 \Rightarrow \text{concave up}; \quad f''(x) < 0 \Rightarrow \text{concave down}$	no restriction stated

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