Find the Tangent Given the Point (2,-2)

Problem

y=x2−4*x+2,(2,−2)

Solution

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

2. Find the derivative of the function y=x2−4*x+2 to determine the general slope formula.

d(y)/d(x)=2*x−4

3. Calculate the slope m at the specific point by substituting x=2 into the derivative.

m=2*(2)−4

m=0

4. Apply the point-slope formula y−(y_0)=m*(x−(x_0)) using the point (2,−2) and the slope m=0

y−(−2)=0*(x−2)

5. Simplify the equation to find the final form of the tangent line.

y+2=0

y=−2

Final Answer

y=−2

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