Find the Tangent Line at the Point y=3x^3-2x , (1,1)

Problem

y=3*x3−2*x,(1,1)

Solution

1. Find the derivative of the function to determine the slope of the tangent line at any point x

d(y)/d(x)=(d(3)*x3−2*x)/d(x)

d(y)/d(x)=9*x2−2

2. Evaluate the derivative at x=1 to find the specific slope m at the given point.

m=9*(1)2−2

m=7

3. Use the point-slope form y−(y_1)=m*(x−(x_1)) with the point (1,1) and the slope m=7

y−1=7*(x−1)

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

y−1=7*x−7

y=7*x−6

Final Answer

y=7*x−6

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