Tangent Line at a Point 2

Geometry Level 1

Which of the following is the tangent line to the curve f ( x ) = 2 x 3 8 x 2 f(x)=2x^3-8x^2 at the point ( 1 , 6 ) ? (1,-6)?

y + 10 x = 4 y + 10x = 4 y 10 x = 4 y - 10x = 4 y 10 x = 4 y - 10x = -4 y + 10 x = 4 y + 10x = -4

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1 solution

Brilliant Mathematics Staff
Jul 31, 2020

Since f ( x ) = 6 x 2 16 x and f ( 1 ) = 10 , f'(x)=6x^2-16x \text{ and } f'(1)=-10, the equation of the tangent line is y + 6 = 10 ( x 1 ) or y + 10 x = 4. y+6=-10(x-1) \text{ or } y+10x=4.

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