Use linear approximation, i.e. the tangent line, to approximate 14.4^2 as follows:

Let f(x)=x^2 and find the equation of the tangent line to f(x) at x=14. Using this, find your approximation for 14.4^2

Question

Use linear approximation, i.e. the tangent line, to approximate 14.4^2 as follows:

Let f(x)=x^2 and find the equation of the tangent line to f(x) at x=14. Using this, find your approximation for 14.4^2

anonymous · Answer

f(x+h) - f(x) = h*f'(x)

if h = 0.4, x = 14, f(x) = x^2

f'(x) = 2*x

so (x + 0.4)^2 - x^2 = 0.4*2*x

thus 14.4^2 = 14^2 + 0.4*2*14

= 196 + 0.8*14

= 196 + 112/10

= 196 + 11.2 = 207.2

anonymous · Answer

excellent, thanks!

anonymous · Answer

the real value of 14.4^2 is 207.36

so the error is very small and approximation is quite good