Asked by Anonymous
Use tangent line approximation to estimate fourth root of 2390 (to seven decimal places) recognizing that 7^4=2401. Show all your work.
Answers
Answered by
oobleck
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.
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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.