Question #7cc4e

1 Answer
Nov 3, 2016

Answer:

#-4x+2h+2#

Explanation:

Question
Find #(f(x+h)-f(x))/h, h!=0#
for #f(x)=-2x^2+2x-4#

Solution
For #f(x)= -2x^2+2x-4#

#{: (f(x+h)," = ",-2(x+h)^2,+2(x+h),-4), (, ,,,), (," = ",-2x^2-4xh-2h^2,+2x+2h,-4), (underline(f(x))," = ",underline(-2x^2color(white)(-4xh-2h^2)),underline(+2xcolor(white)(+2h)),underline(-4)), (f(x+h)-f(x)," = ",color(white)(-2x^2+)-4xh+2h^2,color(white)(+2x)+2h,) :}#

#(f(x+h)=f(x))/h = -4x+2h+2#