Find the difference quotient?

Question

# f (x) = 6 x^2 - 3#

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Answer 1 · 2018-04-25T18:51:47

#12x+6h larr# this is the difference quotient.

Given #f (x) = 6 x^2 - 3#, then #f(x+h) = 6(x+h)^2-3#

Simplify #f(x+h)#:

#f(x+h) = 6x^2+12hx+6h^2-3#

The difference quotient is:

#(f(x+h)-f(x))/h#

Substitute #f(x+h) and f(x)# into the difference quotient:

#(6x^2+12hx+6h^2-3-(6 x^2 - 3))/h#

Distribute the minus sign:

#(6x^2+12hx+6h^2-3-6 x^2 + 3)/h#

Combine like terms:

#(12hx+6h^2)/h#

Factor the numerator:

#(h(12x+6h))/h#

#h/h# becomes 1:

#12x+6h larr# this is the difference quotient.