Find the Tangent Given the Point (1,2)

Problem

y=x2+1,(1,2)

Solution

1. Identify the function and the point ((x_0),(y_0))=(1,2)

2. Find the derivative of the function y=x2+1 to determine the slope formula.

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

3. Calculate the slope m at the given point by substituting x=1 into the derivative.

m=2*(1)

m=2

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

y−2=2*(x−1)

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

y−2=2*x−2

y=2*x

Final Answer

y=2*x

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