f(x)=x^(4/5)
2 Answers

y – y(a) = m(x – a)
f (x) = x^(4/5)
f ‘(x) = (4/5)x^(1/5)
f ‘(a = 32) = (4/5)(32)^(1/5) = (4/5)(1/2) = 4/10 = 2/5
y = m(x – a) + y(a)
y = (2/5)(x – 32) + 16

The equation for the linearization of a function at x = a is:
L(x) = f(a) + f ‘ (a) * (x – a)
f ‘ (x) = (4/5)x^(1/5)
f ‘ (32) = (4/5)(32)^(1/5)
= (4/5)(1/2)
= 2/5
L(x) = f(32) + f ‘ (32) * (x – a)
L(x) = 16 + (2/5) * (x – 32)
L(x) = 16 + (2/5)x – 64/5
L(x) = (2/5)x + 16/5
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Source(s): Linearization: