Question

The point on the curve $y=$ $3x^2+2x+5$ at which the tangent is perpendicular to the line $x+2y+3=0$.

• A. $(0,-5)$
• B. $(0,5)$
• C. $(-5,0)$
• D. $(5,0)$

Answer 1

The correct option is B $(0,5)$

Given curve $y=3x^2+2x+5$

slope $\left(x\right)=\frac{dy}{dx}=\frac{d}{dx}(3x^2+2x+5)=6x+2$

Given tangent is perpendicular to $x+2y+3=0$ slope = $-\frac{1}{2}$

Tangent slope = 2

$\therefore 6x+2=2\Rightarrow x=0$

$\therefore y=3(0{)}^2+2(0)+5=5$

$\therefore$ point on curve = (0,5)