How do you find f'(x) using the definition of a derivative for #f(x)= 10 #?

Question

How do you find f'(x) using the definition of a derivative for #f(x)= 10  #?

HIX Tutor · Accepted Answer

undefined To find f'(x) using the definition of a derivative for f(x) = 10, you follow these steps:

1. Write down the definition of a derivative: f'(x) = lim (h -> 0) [f(x + h) - f(x)] / h
2. Plug in f(x) = 10 into the formula: f'(x) = lim (h -> 0) [10 - 10] / h
3. Simplify the expression: f'(x) = lim (h -> 0) 0 / h
4. Further simplify to find the derivative: f'(x) = lim (h -> 0) 0 = 0

Therefore, the derivative f'(x) of f(x) = 10 is 0.

Ezra Adams · Answer

See the explanation.

#f'(x)=lim_(h->0) (f(x+h)-f(x))/h# #f'(x)=lim_(h->0) (10-10)/h =lim_(h->0) 0/h =lim_(h->0) 0 = 0#

Ezekiel Alexander · Answer

undefined Since $ f(x) = 10 $ is a constant function, its derivative, $ f'(x) $, is equal to 0. This is because the definition of a derivative involves finding the limit of the difference quotient as $ h $ approaches 0, but in the case of a constant function, the value of the function does not change with respect to $ x $, hence the derivative is 0. Therefore, $ f'(x) = 0 $.