Find the Tangent Line at the Point y=8 square root of x , (16,32)

Problem

y=8√(,x),(16,32)

Solution

1. Identify the function and the given point ((x_0),(y_0))=(16,32)

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

y=8*x(1/2)

3. Find the derivative of the function to determine the slope formula.

d(y)/d(x)=8⋅1/2*x(−1/2)

d(y)/d(x)=4/√(,x)

4. Calculate the slope m by substituting x=16 into the derivative.

m=4/√(,16)

m=4/4

m=1

5. Apply the point-slope formula y−(y_0)=m*(x−(x_0)) using the point (16,32) and slope m=1

y−32=1*(x−16)

6. Simplify the equation into slope-intercept form.

y−32=x−16

y=x+16

Final Answer

y=x+16

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