Linear approximation

Question

Use linear approximation, i.e the tangent line, to approximate 3sqrt 8.02 as follows. Let f(x)=3sqrtx and find the equation of the tangent line to f(x) at x=8 in the form y=mx+b.

m =

b=

using these values find the approximation 3sqrt 8.02

Answer 1

a = 8

L(x) = f(a)+f'(a)(x-a)

f'(x)= 3/(2√x)

m=f'(a)

b=f(a)

f(8.02) ≈ b+m(8-8.02)

I'll let you finish the calculation