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Based on the graph, which of the following guarantees that an estimate using tangent line approximation will result in an overestimate? point of tangency near x = -2 point of tangency near x = 0 point of tangency near x = 2 point of tangency near x = 4

Respuesta :

The value of x at which the tangent line approximation will result in an overestimate is given by:

Point of tangency near x = 0.

When does the tangent line approximation results in an underestimate and when does it results in an overestimate?

The possible results for the tangent line approximation are given as follows:

  • Underestimate: tangent line is below the curve.
  • Overestimate: tangent line is above the curve.

The underestimate or underestimate depend on the second derivative of the function, as follows:

  • Second derivative positive: underestimate.
  • Second derivative negative: overestimate.

Hence, regarding the concavity, we have that the definitions are listed as follows:

  • Concave down: overestimate.
  • Concave up: underestimate.

On the graph given by the image at the end of the answer, the concave down point is given as follows:

x = 0.

Hence the correct option is:

Point of tangency near x = 0.

Missing Information

The graph is given by the image at the end of the answer.

More can be learned about concavity at https://brainly.com/question/24430369

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