According to Fermat's Theorem: If f has a local maximum or minimum at c, and if f'(c) exists, then f'(c) = 0. However, we must be careful when using Fermat's Theorem. Even when f'(c) = 0 there need not be a maximum or minimum at c. Furthermore, there may be an extreme value even when f'(c) does not exist. Give two examples (one of each) of specific functions f and values of c that demonstrate the following two cases: 1. f'(c) = 0 but f has no maximum or minimum at c 2. f has a maximum or minimum at c but f'(c) does not exist
According to Fermat's Theorem: If f has a local maximum or minimum at c, and if f'(c) exists, then f'(c) = 0. However, we must be careful when using Fermat's Theorem. Even when f'(c) = 0 there need not be a maximum or minimum at c. Furthermore, there may be an extreme value even when f'(c) does not exist. Give two examples (one of each) of specific functions f and values of c that demonstrate the following two cases: 1. f'(c) = 0 but f has no maximum or minimum at c 2. f has a maximum or minimum at c but f'(c) does not exist
According to Fermat's Theorem: If f has a local maximum or minimum at c, and if f'(c) exists, then f'(c) = 0. However, we must be careful when using Fermat's Theorem. Even when f'(c) = 0 there need not be a maximum or minimum at c. Furthermore, there may be an extreme value even when f'(c) does not exist. Give two examples (one of each) of specific functions f and values of c that demonstrate the following two cases: 1. f'(c) = 0 but f has no maximum or minimum at c 2. f has a maximum or minimum at c but f'(c) does not exist
According to Fermat's Theorem: If f has a local maximum or minimum at c, and if f'(c) exists, then f'(c) = 0. However, we must be careful when using Fermat's Theorem. Even when f'(c) = 0 there need not be a maximum or minimum at c. Furthermore, there may be an extreme value even when f'(c) does not exist.
Give two examples (one of each) of specific functions f and values of c that demonstrate the following two cases:
1. f'(c) = 0 but f has no maximum or minimum at c
2. f has a maximum or minimum at c but f'(c) does not exist
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
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