Asked by James
Use linear approximation, i.e. the tangent line, to approximate cubed root { 1.1 }. The equation of the tangent line to f(x) at x = 1 can be written in the form y = mx+b.
Show your work. Do not use a calculator.
Show your work. Do not use a calculator.
Answers
Answered by
Damon
y = x^(1/3)
dy/dx = (1/3) x^-(2/3)
at x = 1, y = 1 and dy/dx = (1/3)=m
y = 1 + (1/3) (x-1)
y = (1/3) x + 2/3
at x = 1.1
y = (1/3)(1.1) + 2/3
y = (1/3) 3.1
dy/dx = (1/3) x^-(2/3)
at x = 1, y = 1 and dy/dx = (1/3)=m
y = 1 + (1/3) (x-1)
y = (1/3) x + 2/3
at x = 1.1
y = (1/3)(1.1) + 2/3
y = (1/3) 3.1
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