Question

(1 point) Suppose that $f(x, y)$ is a differentiable function and that its partial derivatives have the values $f_x(4, -7) = 3$ and $f_y(4, -7) = 2$. Given that $f(4, -7) = -4$, use this information to estimate the following values: Estimate of $f(4, -6)$: Estimate of $f(5, -7)$: Estimate of $f(5, -6)$:

          (1 point)
Suppose that $f(x, y)$ is a differentiable function and that its partial derivatives have the values
$f_x(4, -7) = 3$ and $f_y(4, -7) = 2$. Given that $f(4, -7) = -4$, use this information to estimate
the following values:
Estimate of $f(4, -6)$:
Estimate of $f(5, -7)$:
Estimate of $f(5, -6)$:

(1 point)
Suppose that f(x, y) is a differentiable function and that its partial derivatives have the values
fx(4, -7) = 3 and fy(4, -7) = 2. Given that f(4, -7) = -4, use this information to estimate
the following values:
Estimate of f(4, -6):
Estimate of f(5, -7):
Estimate of f(5, -6):

Added by Danielle P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

12/03/2022

Step 1

Step 1: Calculate the estimate of $f(4, 6)$ using the linear approximation formula: \[ l(x, y) = f(4, 7) + f_x(4, 7)(x - 4) + f_y(4, 7)(y - 7) \] \[ l(x, y) = 3 + 3(x - 4) + 2(y - 7) \] \[ l(4, 6) = 3 + 3(4 - 4) + 2(6 - 7) \] \[ \textbf{l(4, 6) = 3} \] Show more…

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Suppose that f(x, y) is a differentiable function and that its partial derivatives have the values fx(4, -7) = 3 and fy(4, -7) = 2. Given that f(4, -7) = -4, use this information to estimate the following values Estimate of f(4, -6) Estimate of f(5, -7) Estimate of f(5, -6)