Find the Tangent Line at the Point y=4x^3-4x , (-1,0)

Problem

y=4*x3−4*x,(−1,0)

Solution

1. Identify the given function y=4*x3−4*x and the point ((x_1),(y_1))=(−1,0)

2. Find the derivative of the function to determine the slope formula for the tangent line.

d(y)/d(x)=12*x2−4

3. Calculate the slope m by substituting the xcoordinate of the given point, x=−1 into the derivative.

m=12*(−1)2−4

m=12*(1)−4

m=8

4. Apply the point-slope formula y−(y_1)=m*(x−(x_1)) using m=8 and the point (−1,0)

y−0=8*(x−(−1))

5. Simplify the equation into slope-intercept form.

y=8*(x+1)

y=8*x+8

Final Answer

y=8*x+8

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