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

Problem

y=3*x3−5*x,(1,−2)

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)*x3−5*x)/d(x)

d(y)/d(x)=9*x2−5

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

m=9*(1)2−5

m=4

3. Use the point-slope formula y−(y_1)=m*(x−(x_1)) with the point (1,−2) and the slope m=4

y−(−2)=4*(x−1)

y+2=4*x−4

4. Solve for y to write the equation in slope-intercept form.

y=4*x−6

Final Answer

y=4*x−6

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