Question

The equation of the tangent to the curve $y = x^3 - 6x + 5$ at $(2,1)$ is

• A. 6x - y - 11 = 0
• B. 6x - y - 13 = 0
• C. 6x + y + 11 = 0
• D. 6x - y + 11 = 0

Answer 1

Answer: (A)

6x - y - 11 = 0

Answer 2

The equation of the curve $y=x^{3}-6 x+5$ $\Rightarrow \frac{d y}{d x}=3 x^{2}-6$ $\Rightarrow \left(\frac{d y}{d x}\right)_{(2,1)}=6$ Now, equation of the tangent at $(2,1)$ is $(y-1)=6(x-2)$ $\Rightarrow y-1=6 x-12$ $\Rightarrow 6 x-y-11=0$