How do you use the definition of a derivative to find the derivative of #f(x)= 2x^2 - 3x+4#? Calculus Derivatives Limit Definition of Derivative 1 Answer Steve M Oct 31, 2016 # f'(x) = 4x-3# Explanation: By definition # f'(x) =lim_(hrarr0)( (f(x+h)-f(x))/h ) # So, with # f(x)=2x^2-3x+4 # we have: # f'(x) = lim_(hrarr0)( ( (2(x+h)^2-3(x+h)+4) - (2x^2-3x+4) ) / h ) # # :. f'(x) = lim_(hrarr0)( ( ( 2(x^2+2hx+h^2)-3x-3h+4) - (2x^2-3x+4) ) /h )# # :. f'(x) = lim_(hrarr0)( ( 2x^2+4hx+2h^2-3x-3h+4 - 2x^2+3x-4) /h )# # :. f'(x) = lim_(hrarr0)( ( 4hx+2h^2-3h) /h )# # :. f'(x) = lim_(hrarr0)( 4x+2h-3 )# # :. f'(x) = 4x-3# Answer link 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 1301 views around the world You can reuse this answer Creative Commons License