Find the Tangent Line at the Point y = square root of 2x , (18,6)

Problem

y=√(,2*x),(18,6)

Solution

1. Rewrite the function in power form to prepare for differentiation.

y=(2*x)(1/2)

2. Apply the chain rule to find the derivative of the function, which represents the slope of the tangent line.

d(y)/d(x)=1/2*(2*x)(−1/2)⋅2

3. Simplify the derivative expression.

d(y)/d(x)=1/√(,2*x)

4. Evaluate the derivative at the given point x=18 to find the specific slope m

m=1/√(,2*(18))

m=1/√(,36)

m=1/6

5. Use the point-slope formula y−(y_1)=m*(x−(x_1)) with the point (18,6) and slope m=1/6

y−6=1/6*(x−18)

6. Solve for y to write the equation in slope-intercept form.

y−6=1/6*x−3

y=1/6*x+3

Final Answer

y=1/6*x+3

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