Find the Tangent Line at the Point y=x^2+6 , (1,7)

Problem

y=x2+6,(1,7)

Solution

1. Identify the function and the given point ((x_0),(y_0))=(1,7)

2. Find the derivative of the function to determine the slope formula for any point x

(d(x2)+6)/d(x)=2*x

3. Calculate the slope m at the specific 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 (1,7) and the slope m=2

y−7=2*(x−1)

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

y−7=2*x−2

y=2*x+5

Final Answer

y=2*x+5

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