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What is the equation of the tangent line of #y=(x-1)^3# at #x=2#?

Answer 1

Christopher Agresta

y = 3x - 5

The tangent's equation is as follows: y - b = m (x - a).

where m denotes the line's gradient, or slope, and

(a, b) is a line point where the x-coordinate is known.

Enter x = 2 into the equation to find y. To find m

After differentiating the function, assess it for x = 2.

Using #color(blue)(" ' chain rule '") #

# dy/dx = 3(x - 1 )^2 .d/dx (x - 1 ) = 3(x - 1 )^2 .1 = 3(x - 1 )^2#

x = 2 : # m = dy/dx = 3( 2 - 1 )^2 = 3 #

and y = # (2 - 1 )^3 = 1 #

The tangent equation is as follows: y - b = m (x - a), m = 3, (a, b ) = (2, 1 ).

y - 1 = 3 (x - 2) as a result, making y - 1 = 3x - 6.

# rArr y = 3x - 5 #

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Answer 2

Adam Adkins

The equation of the tangent line of y=(x-1)^3 at x=2 is y = 9x - 17.

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