Use the equation of the line tangent to h(x) = √x - 6 at the point (10, 2) to approximate h(9.5). Round...

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Use the equation of the line tangent to h(x) = √x - 6 at the point (10, 2) to approximate h(9.5). Round answers expressed as decimals to the nearest thousandth. h(9.5) ≈

SnapAndSolve AI · Accepted Answer

To find the tangent line at the point (10, 2), we first need the derivative of h(x) = √x - 6, which is h'(x) = 1/(2√x).

At x = 10, h'(10) = 1/(2√10) = 1/6.3246 ≈ 0.158.

The equation of the tangent line is y - 2 = 0.158(x - 10).

Simplifying, y = 0.158x - 1.58.

To approximate h(9.5), substitute x = 9.5 into the tangent line equation:

y = 0.158(9.5) - 1.58 ≈ 1.501 - 1.58 ≈ 1.921.

Thus, h(9.5) ≈ 1.921.

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Use the equation of the line tangent to h(x) = √x - 6 at the point (10, 2) to approximate h(9.5). Round...

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