Find the Tangent Line at the Point y=3x^3-4x , (1,-1)

Problem

y=3*x3−4*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)*x3−4*x)/d(x)

d(y)/d(x)=9*x2−4

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

m=9*(1)2−4

m=5

3. Use the point-slope form of a linear equation, y−(y_1)=m*(x−(x_1)) substituting the point (1,−1) and the slope m=5

y−(−1)=5*(x−1)

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

y+1=5*x−5

y=5*x−6

Final Answer

y=5*x−6

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