M Mswen New member Joined Sep 30, 2013 Messages 1 Sep 30, 2013 #1 Find: f(a+h) - f(a) _________ h if h does not equal zero f(x) = -x^2 + x +5 The very first thing is supposed to be all over h
Find: f(a+h) - f(a) _________ h if h does not equal zero f(x) = -x^2 + x +5 The very first thing is supposed to be all over h
J JeffM Elite Member Joined Sep 14, 2012 Messages 7,875 Sep 30, 2013 #2 Mswen said: Find: f(a+h) - f(a) _________ h if h does not equal zero f(x) = -x^2 + x +5 The very first thing is supposed to be all over h Click to expand... \(\displaystyle \dfrac{f(x + h) - f(x)}{h},\ h \ne 0\) is a template, a recipe, into which you put whatever function is specified. In fact, that template is a way to define a new kind of function from a given function. In this case, \(\displaystyle f(x) = -x^2 + x + 5 \implies f(x + h) = - (x + h)^2 + (x + h) + 5.\) Simple, no? So \(\displaystyle \dfrac{f(x + h) - f(x)}{h} = \dfrac{- (x + h)^2 + (x + h) + 5 - (-x^2 + x + 5)}{h}.\) The rest is just algebra. Sometimes the algebra is hard; sometimes it is easy.
Mswen said: Find: f(a+h) - f(a) _________ h if h does not equal zero f(x) = -x^2 + x +5 The very first thing is supposed to be all over h Click to expand... \(\displaystyle \dfrac{f(x + h) - f(x)}{h},\ h \ne 0\) is a template, a recipe, into which you put whatever function is specified. In fact, that template is a way to define a new kind of function from a given function. In this case, \(\displaystyle f(x) = -x^2 + x + 5 \implies f(x + h) = - (x + h)^2 + (x + h) + 5.\) Simple, no? So \(\displaystyle \dfrac{f(x + h) - f(x)}{h} = \dfrac{- (x + h)^2 + (x + h) + 5 - (-x^2 + x + 5)}{h}.\) The rest is just algebra. Sometimes the algebra is hard; sometimes it is easy.
