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selected values of the derivative of the function g are given in the table above. it is known that g(4)=12. what is the approximation for g(4.2) found using the line tangent to the graph of g at x=4 ?

Sagot :

Vinodhiniss

The approximation for the function g(4.2) is 12.44

What is the approximation for the function?

From the table, we know that g'(4) = 2.2

g (4) = 12

Using the line tangent to the graph of g at x=4 ,

g (4.2)  = g (4 ) + (4.2 -4 )2.2

           = 12 + 0.44

           = 12.44

The approximation for the function g(4.2) is 12.44. So ,option A is correct.

What is a tangent?

  • The graph of the affine function that most closely resembles the original function at the specified location is known as a tangent line approximation.
  • It can be thought of as the tangent line to a point on a differentiable curve.
  • The plane that touches a surface at a specific location is known as the tangent plane to that surface.
  • One of differential geometry's most basic ideas is the idea of a tangent.
  • Differentiability is a particular kind of mathematical smoothness that is essential to the tangent line's existence and uniqueness.
  • The point of tangency, where the tangent line and the curve converge, is where the tangent passes through.
  • Refer image for complete question.

To learn more about tangent, refer:

https://brainly.com/question/4470346

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