Find the Tangent Line at the Point y=16 square root of x , (16,64)

Problem

y=16√(,x),(16,64)

Solution

1. Rewrite the function using a fractional exponent to make differentiation easier.

y=16*x(1/2)

2. Differentiate the function with respect to x using the power rule to find the slope formula.

d(y)/d(x)=16⋅1/2*x(−1/2)

3. Simplify the derivative expression.

d(y)/d(x)=8/√(,x)

4. Evaluate the derivative at the given xcoordinate x=16 to find the slope m of the tangent line.

m=8/√(,16)

m=8/4

m=2

5. Apply the point-slope formula y−(y_1)=m*(x−(x_1)) using the point (16,64) and the slope m=2

y−64=2*(x−16)

6. Simplify the equation into slope-intercept form y=m*x+b

y−64=2*x−32

y=2*x+32

Final Answer

y=2*x+32

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