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

Problem

y=4*x3−3*x,(1,1)

Solution

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

d(y)/d(x)=(d(4)*x3−3*x)/d(x)

d(y)/d(x)=12*x2−3

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

m=12*(1)2−3

m=9

3. Use the point-slope form y−(y_1)=m*(x−(x_1)) with the point (1,1) and the slope m=9

y−1=9*(x−1)

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

y−1=9*x−9

y=9*x−8

Final Answer

y=9*x−8

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