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

Problem

y=2*x3−5*x,(1,−3)

Solution

1. Find the derivative of the function to determine the slope of the tangent line at any point x

d(y)/d(x)=6*x2−5

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

m=6*(1)2−5

m=1

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

y−(−3)=1*(x−1)

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

y+3=x−1

y=x−4

Final Answer

y=x−4

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