For y = f(x) = 2x - 1, x = 5, and △x = 3 find
a) △y for the given x and △x values,
b) dy = f'(x)dx,
c) dy for the given x and △x values.
SOLUTION :
y = f(x) = 2x - 1
=> f’ (x) = 2
a.
Now,
f’ (x) = dy / dx ≈ ∆y / ∆x
=> ∆y ≈ f’ (x) ∆x
=> ∆y (at x = 5, ∆x = 3) is = 2 * 3
=> ∆y = 6 (ANSWER).
b.
dy = f’(x) dx = 2 dx (ANSWER).
c.
dy ≈ ∆y = 6 (ANSWER)
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