Solved: "How do you use the definition of a..."

Jewel Beard

Answered question

2022-04-09

How do you use the definition of a derivative to find the derivative of f(x)=6?

superpms01wks1

Beginner2022-04-10Added 13 answers

The definition of derivative is:

lim_{h \to 0} \frac{f (x + h) - f (x)}{h} = f^{'} (x)

.
So:

lim_{h \to 0} \frac{6 - 6}{h} = 0

prangijahnot

Beginner2022-04-11Added 17 answers

The definition of derivative tells you that:

f^{'} (x) = lim_{△ x \to 0} \frac{f (x + △ x) - f (x)}{△ x}

where

△ x

is an increment of x corresponding
to an increment of your function

f (x + △ x)

.
Your function is a constant so you have that:
f(x)=6

f (x + △ x) = 6

i.e. your function has always the same value, 6;
You can now write:

f^{'} (x) = lim_{△ x \to 0} \frac{f (x + △ x) - f (x)}{△ x} =

f^{'} (x) = lim_{△ x \to 0} \frac{6 - 6}{△ x} = 0

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