# ch3 - y = x 3 2 x 1 at x = 2 The slope of the tangent line...

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Find the equation of the tangent line for y = x 2 + 6 at x = 3 The slope of the tangent line at any point is the derivative at that point Solution: y ' = 2 x 3 At x = 3, we need to find m and y : x = 3 then m =y ' (3) = 2(3) = 6 Now we want to find the equation of the line that passes the point ( x =3, y =15) with m = 6 x = 3 then y (3) = (3) 2 + 6 = 15 y = mx + b 15 = (6)(3) + b -3 = b The equation of the tangent line at x = 3 is: y = 6 x - 3 15 Note: The following examples are part of sections 3.1 - 3.3 homework

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Find the equation of the tangent line for
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Unformatted text preview: y = x 3- 2 x + 1 at x = 2 The slope of the tangent line at any point is the derivative at that point Solution: y ' = 3 x 2- 2 At x = 2, we need to find m and y : x = 2 then m =y ' (2) = 3(2) 2- 2 = 10 Now we want to find the equation of the line that passes the point ( x = 2, y = 5) with m = 10 x = 2 then y (2) = (2) 3 -2(2) + 1= 5 y = mx + b 5 = (10)(2) + b-15 = b The equation of the tangent line at x = 2 is: y = 10 x - 15 5...
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ch3 - y = x 3 2 x 1 at x = 2 The slope of the tangent line...

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