Find the Tangent Line at the Point y=5x^3-2x , (1,3)

Problem

y=5*x3−2*x,(1,3)

Solution

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

d(y)/d(x)=15*x2−2

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

m=15*(1)2−2

m=13

3. Use the point-slope form of a linear equation, y−(y_1)=m*(x−(x_1)) with the point (1,3) and the slope m=13

y−3=13*(x−1)

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

y−3=13*x−13

y=13*x−10

Final Answer

y=13*x−10

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