How to Find local Maximum and Minimum Point when Rational Function l Critical Point l Calculus

Fermat’s theorem

If the function has the local minimum or maximum at point C and if the function has the first derivative (differentiable) at point C, then 𝒇^′ (𝑪)=𝟎
Theorem(First Derivative Test)

Let 𝒇 :𝚰→ℝ ,𝚰⊆ℝ be differentiable function on 𝚰 and 𝑪∈ 𝚰 a critical number.

If 𝒇^′ (𝑪) changes sign from positive to negative around number C, then (𝑪 , 𝒇(𝑪))
is the local maximum

If 𝒇^′ (𝑪) changes sign from negative to positive around number C, then (𝑪 , 𝒇(𝑪))
is the local minimum

If 𝒇^′ (𝑪) has the same sign from both sides of C, then the local extremum does not exists at C
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Define Global/Absolute Maximum and Minimum l How to Find the Absolute Maximum and Minimum l Example

How to Find the Absolute Maximum and Minimum l How to Find the Global Maximum and Minimum l Example

Define Critical Point with Examples l Types of Critical Points l Local Maxima and Minima l

Define inflection point l what is inflection point with example l Critical Point l

How to find critical Point l How to find local maxima l How to find local maximum point l

How to find critical Point l How to find local Minima l How to find local

Continuity of a function at a point l Explanation l Example l Matlab Code

Explain Types of Discontinuities l Function l Continuity l Types of Discontinuities l Calculus

Types of Continuities l Classification of Continuities l Discontinuities l Types l Calculus