Q106 / 160 · AP EAMCET 2024 (21 May Shift 2) · Mathematics

The equation of the tangent to the curve $y=x^3-2 x+7$ at the point $(1,6)$ is

Correct answer
A
$y=x+5$
B
$2 x+y=8$
C
$x+y=7$
D
$x+2 y=13$

Solution

$y=x^3-2 x+7 \Rightarrow \frac{d y}{d x}=3 x^2-\left.2 \Rightarrow \frac{d y}{d x}\right|_{x=1}=1$ Equation of tangent is
$\frac{y-6}{x-1}=1 \Rightarrow x-y+5=0 \Rightarrow y=x+5$

Hence, the correct answer is option: 'A'.

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