How do you find f'(x) using the definition of a derivative for #f(x)= -7x^2 + 4x #? Calculus Derivatives Limit Definition of Derivative 1 Answer Konstantinos Michailidis Sep 27, 2015 See explanation Explanation: It is #f'(x)=lim_(h->0) ((f(x+h)-f(x))/h) => f'(x)=lim_(h->0)(-7*(x+h)^2+4(x+h)-(-7x^2+4x))/h=> f'(x)=lim_(h->0) ((-h(7h+2*(7x-2)))/h)=> f'(x)=lim_(h->0) (-(7h+2(7x-2)))=> f'(x)=-14x+4# 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 1477 views around the world You can reuse this answer Creative Commons License