Find the Tangent Line at the Point y = square root of x , (1,1)

Problem

y=√(,x),(1,1)

Solution

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

2. Find the derivative of the function y=√(,x) to determine the slope of the tangent line at any point x

d(√(,x))/d(x)=1/(2√(,x))

3. Calculate the slope m by substituting the xcoordinate of the given point into the derivative.

m=1/(2√(,1))

m=1/2

4. Apply the point-slope formula y−(y_0)=m*(x−(x_0)) using the point (1,1) and the slope m=1/2

y−1=1/2*(x−1)

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

y−1=1/2*x−1/2

y=1/2*x+1/2

Final Answer

y=1/2*x+1/2

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