Question

If tangent at a point of the curve $y=f\left(x\right)$ is perpendicular to $2x-3y=5$ then at that point $\frac{dy}{dx}$ equals

• A. $\frac{2}{3}$
• B. $-\frac{2}{3}$
• C. $\frac{3}{2}$
• D. $-\frac{3}{2}$

Answer 1

Answer: (D)

$-\frac{3}{2}$

We know slope of tangent to the curve is $\frac{dy}{dx}$
Now slope of line $2x-3y=5$ is $\frac{2}{3}$
and tangent to $y=f\left(x\right)$ is perpendicular to this line.
$\therefore$ $\frac{dy}{dx}=-\frac{3}{2}$
Hence, option 'D' is correct.