Find the Tangent Line at the Point y=x^3-3x , (2,2)

Problem

y=x3−3*x,(2,2)

Solution

1. Find the derivative of the function to determine the general slope formula.

d(y)/d(x)=3*x2−3

2. Evaluate the derivative at the given xcoordinate, x=2 to find the slope of the tangent line m

m=3*(2)2−3

m=3*(4)−3

m=9

3. Use the point-slope form y−(y_1)=m*(x−(x_1)) with the point (2,2) and the slope m=9

y−2=9*(x−2)

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

y−2=9*x−18

y=9*x−16

Final Answer

y=9*x−16

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