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for the functions given below, find and simplify completely: g(x+h)-g(x)/h (here, h is some parameter)
a. g(x) = 2x +6
b. g(x) = 2x^2-x

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a. 2

b. 4x -1 +2h

Step-by-step explanation:

We can find the difference quotient for the given cases by first solving for the difference quotient in the general case. That solution can then be applied to the given cases.


general solution

For f(x) = ax² +bx +c, the difference quotient is ...




For g(x) = 2x+6, we have a=0, b=2, c=6. Substituting these values into the above formula, we find ...

(g(x+h) -g(x))/h = 2·0·x² +2 +0·h

(g(x+h) -g(x))/h = 2



For g(x) = 2x² -x, we have a=2, b=-1, c=0. Substituting these values into the above formula, we find ...

(g(x+h) -g(x))/h = 2·2·x +(-1) +2·h

(g(x+h) -g(x))/h = 4x -1 +2h
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