(a)

The function is  and the point is .

Apply derivative on each side with respect to .

Apply power rule of differentiation: .

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Slope of the tangent line is the derivative of the function at .

Substitute in the derivative function.

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Slope of the tangent line to the curve at the point is .

Find the tangent line.

Point-slope form of line equation : .

Substitute and in point-slope form.

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The tangent line is .

(b)

Graph:

Graph the function and tangent line passing through the point .

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(c)

Graph:

Graph the derivative field .

Graph the function and tangent line passing through the point .

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(a) The tangent line equation is  .

(b)

Graph:

Graph the function and tangent line passing through the point .

(c) Graph the derivative field .

Graph the function and tangent line passing through the point .

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