Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you use the limit definition of the derivative to find the derivative of $f (x) = - x + 6$ $f(x)=-x+6$ ?

1 Answer

Sep 26, 2016

$f'(x)=-1$

Explanation:

By definition: $f'(x) = lim_"h->0" (f(x+h)-f(x))/h$

In this example $f(x)=-x+6$

Hence: $f'(x) = lim_"h->0"(-x-h+6+x-6)/h$

$f'(x) = lim_"h->0"(cancel(-x)-hcancel(+6)cancel(+x)cancel(-6))/h$

$f'(x) = lim_"h->0" -h/h =-1$

Related questions

What is the limit definition of the derivative of the function $y=f(x)$ ?
Ho do I use the limit definition of derivative to find $f'(x)$ for $f(x)=3x^2+x$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=sqrt(x+3)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=1/(1-x)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=x^3-2$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=1/sqrt(x)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=5x-9x^2$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=sqrt(2+6x)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=mx+b$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=c$ ?

See all questions in Limit Definition of Derivative

Impact of this question

1365 views around the world

You can reuse this answer
Creative Commons License