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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