Question

difference quotient of function f(x) is defined as :
f(x+h) - f(x)/ h
compute the difference quotient of the given functions
a) y(z) = 1/ z+2
b) g(x)= 6-x^2
please help

Answer 1

the h is the denominator

Answer 2

I think it should be [f(x+h) - f(x)/ ]h instead of f(x+h) - f(x)/ h

Answer 3

I am sorry for the typos
I meant "I think it should be [f(x+h) - f(x) ]/h instead of f(x+h) - f(x)/ h"

Answer 4

yeah iamignorant

Answer 5

y(z +h) -y(z)= 1/(z+h+2) - 1/(z+2)= z+2-z-h-2/(z+h+2)(z+2) = -h/(z+h+2)(z+2)
dividing by h on both sides gives
y(z +h) -y(z)/h = 1/(z+h+2)(z+2)

Answer 6

oh i missed the negative sign in the numerator :)

Answer 7

g(x) = 6 - x^2
g(x+h) = 6-(x +h)^2= 6-x^2-2xh- h^2
g(x+h) - g(x) = -2xh - h^2 = -h(2x +h)
g(x+h) - g(x)/h = 2x +h

Answer 8

do u mind explaining the y(z+h)-y(z) blablabla how it comes about?

Answer 9

replace z by z +h

Answer 10

then simlify the expression by taking the LCM