Find the Tangent Given the Point (-1,-3)

Problem

y=x3+2*x, at *(−1,−3)

Solution

1. Identify the function ƒ(x)=x3+2*x and the given point ((x_0),(y_0))=(−1,−3)

2. Find the derivative of the function to determine the slope formula for any point x

(d(x3)+2*x)/d(x)=3*x2+2

3. Calculate the slope m by substituting the xcoordinate of the given point into the derivative.

m=3*(−1)2+2

m=5

4. Apply the point-slope formula y−(y_0)=m*(x−(x_0)) using the point (−1,−3) and the slope m=5

y−(−3)=5*(x−(−1))

y+3=5*(x+1)

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

y+3=5*x+5

y=5*x+2

Final Answer

y=5*x+2

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