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How do you use the limit definition of the derivative to find the derivative of #f(x)=-4#?

Answer 1

Evelyn Agard

see below

#f'(x) equiv lim_(h to 0) (f(x+h) - f(x))/(h)#

In this case: #f'(x) = lim_(h to 0) (- 4 - (- 4))/(h)#

# = lim_(h to 0) (0)/(h) = 0#

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Answer 2

Adam Adkins

To find the derivative of ( f(x) = -4 ) using the limit definition of the derivative, we apply the formula:

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

Substitute ( f(x) = -4 ) into the formula:

[ f'(x) = \lim_{h \to 0} \frac{-4 - (-4)}{h} ]

Simplify:

[ f'(x) = \lim_{h \to 0} \frac{0}{h} ]

Since the numerator is zero regardless of the value of ( h ), the limit will be zero:

[ f'(x) = 0 ]

Therefore, the derivative of ( f(x) = -4 ) is ( f'(x) = 0 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.