Hello, plainmath! Help please to find answer. Is differentiation of zero, zero? I tried to find the answer but I couldn't.

patryk1987sgp

patryk1987sgp

Answered question

2022-12-17

Hello, plainmath! Help please to find answer.
Is differentiation of zero, zero?
I tried to find the answer but I couldn't.

Answer & Explanation

Landin Mullins

Landin Mullins

Beginner2022-12-18Added 3 answers

f ( x ) = lim h 0 f ( x + h ) f ( x ) h = lim h 0 0 h = 0.
Geometrically speaking, the graph of f : x 0 is a horizontal line, so its slope at each point is zero, hence its derivative is equal to zero everywhere. From another perspective, f : x 0 is a constant function, it doesn't vary, so its rate of change is zero.

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