Question

Find and simplify the difference quotient f(x+h)-f(x)/h,for the function f(x)=-5x^2+7x+16

Answer 1

I think the answer should be -10x +7

Here's my take on it...
[-5(x+h)^2+7(x+h)+16 - (-5x^2+7x +16)]/h
[-5(x^2+2xh+h^2)+7x+7h+16-5x^2-7x-16]/h
=(-10xh-5h^2+7h)/h
dividing each term by h gives:
-10x+7-5h..........At this point it is essential to remember that we are simplifying for when \[\lim_{h \rightarrow 0}\]. In fact this should have been written on every line but is too cumbersome to write here. In considering this we see that the 5h term approaches 0 as h gets closer and closer to 0. hence the solution is the remaining terms -10x +7