Question

Slope of tangent(s) to $y=(x-2)(x+3)(x+4)$ at point(s) where curve intersects the $x-$axis, is/are

• A. $0$
• B. $6$
• C. $-5$
• D. $30$

Answer 1

Answer: (B), (C), (D)

$30$

At $x-$axis $y=0$
$\Rightarrow x=2,-3,-4$
$\Rightarrow \frac{dy}{dx}=(x+3)(x+4)+(x-2)(x+4)+(x-2)(x+3)\frac{dy}{dx}=3x^2+10x-2\Rightarrow {\frac{dy}{dx}|}_{x=2}=3\cdot 4+20-2=30\Rightarrow {\frac{dy}{dx}|}_{x=-3}=3\cdot 9-30-2=-5\Rightarrow {\frac{dy}{dx}|}_{x=-4}=48-40-2=6$