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Sagot :
A nice simple differentiation question!
We are given the function f(x) = -2x + 1.
We need to find the difference quotient:
f(x + h) - f(x) / h
First, let's evaluate f(x + h) and f(x):
f(x + h) = -2(x + h) + 1
= -2x - 2h + 1
f(x) = -2x + 1
Now, let's subtract f(x) from f(x + h):
f(x + h) - f(x) = (-2x - 2h + 1) - (-2x + 1)
= -2h
Now, divide by h:
(f(x + h) - f(x)) / h = (-2h) / h
= -2
So, the difference quotient is -2.
In other words, as x approaches x + h, the function f(x) changes by -2 units for every unit change in x.
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