Use tangent line approximation to estimate fourth root of 2390 (to seven decimal places) recognizing that 7^4=2401. Show all your work.

Answer 1

y = x^(1/4)
y' = 1/4 x^(-3/4)
at (7,2401) y' = -1/1372
so, since ∆y ≈ dy/dx * ∆x,
∆y ≈ (-1/1372)(-11) = 0.00802
making
∜2390 ≈ 7.008
real value: 6.992
makes sense, since the graph is concave down, so the tangent line will overestimate the true value.