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How do you find f'(x) using the definition of a derivative for #-(2/3x) #?

Answer 1

Ezekiel Alexander

Evaluate the limit to find that

#d/dx(-2/3x)=-2/3#

Using the definition #f'(x) = lim_(h->0)(f(x+h)-f(x))/h#

we have

#d/dx(-2/3x) = lim_(h->0)(-2/3(x+h)-(-2/3x))/h#

#=lim_(h->0)-2/3*(x+h-x)/h#

#=lim_(h->0)-2/3*h/h#

#=lim_(h->0)-2/3#

#=-2/3#

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Answer 2

Paisley Johnson

To find the derivative of the function f(x) = -(2/3)x using the definition of a derivative, you would apply the limit definition of the derivative, which is:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

For the given function f(x) = -(2/3)x, you would plug in the function values into this definition and simplify the expression to find f'(x).

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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.