Find the Tangent Line at the Point y=x^3-5x , (2,-2)

Problem

y=x3−5*x,(2,−2)

Solution

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

d(y)/d(x)=3*x2−5

2. Evaluate the derivative at the given xcoordinate, x=2 to find the specific slope m

m=3*(2)2−5

m=3*(4)−5

m=7

3. Use the point-slope form of a linear equation, y−(y_1)=m*(x−(x_1)) with the point (2,−2) and the slope m=7

y−(−2)=7*(x−2)

4. Simplify the equation into slope-intercept form by distributing and isolating y

y+2=7*x−14

y=7*x−16

Final Answer

y=7*x−16

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