Question

use a tangent plane to approximate the value of the following function at the point ( − 4.9 , − 3.1 ) (-4.9,-3.1) . give your answer accurate to 4 decimal places.

Answer 1

The provided information relates to quadratic equations and the quadratic formula, which cannot be used to answer the question about the tangent plane approximation without more details on the function itself.

Step-by-step explanation:

The given question pertains to the use of the tangent plane to approximate the value of a function at a specific point. However, the information provided references quadratic equations and their solutions using the quadratic formula. This formula is at2 + bt + c = 0 and, in this context, doesn't relate to the use of a tangent plane for approximation purposes. The quadratic formula is used to find the values of t that solve the equation, which is typically represented as x = -b ± √b2 - 4ac / (2a). Without the correct function or additional information about the function being approximated by the tangent plane, it is not possible to provide a precise answer to the original question about approximation at the point (-4.9, -3.1).

Answer 2

To approximate the value of a function using a tangent plane, we need the equation of the tangent plane at the given point.

Step-by-step explanation:

To approximate the value of the function at the given point using a tangent plane, we need the equation of the tangent plane at that point. First, let's find the gradient vector of the function. The gradient vector provides the direction of steepest ascent at any point and is normal to the tangent plane. In this case, the given function is not provided, so we are unable to find the gradient vector and proceed with the tangent plane approximation. Please provide the function to receive further assistance.