Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you find the derivative of #f(x) = 7x^2 - 3 # using the limit definition?

1 Answer

Jun 22, 2016

#14x#

Explanation:

f#'(x) = lim_{h \to 0} ( (7(x+h)^2 - 3) - (7x^2 - 3))/h#

# = lim_{h \to 0} ( (7(x^2+2xh + h^2) - 3) - (7x^2 - 3))/h#

# = lim_{h \to 0} ( 7x^2+14xh + 7h^2 - 3 - 7x^2 + 3)/h#

# = lim_{h \to 0} ( 14xh + 7h^2 )/h#

# = lim_{h \to 0} 14x + 7h = 14x#

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

4772 views around the world

You can reuse this answer
Creative Commons License