Find the slope of the polar curve at the indicated point.
-$$r = 6 ( 1 + \cos \theta ) , \theta = \frac { \pi } { 4 }$$
A) $1 - \sqrt { 2 }$
B) $4 \sqrt { 2 }$
C) $\frac { \sqrt { 3 } } { 3 }$
D) $- 2$

Question

Quizplus · Accepted Answer

The slope of a polar curve $r = f(\theta)$ at a given point can be found using the formula $\frac{dy}{dx} = \frac{f'(\theta) \sin(\theta) + f(\theta) \cos(\theta)}{f'(\theta) \cos(\theta) - f(\theta) \sin(\theta)}$. For $r = 6(1 + \cos(\theta))$, $f'(\theta) = -6\sin(\theta)$. Substituting $\theta = \frac{\pi}{4}$ and simplifying gives the slope as $1 - \sqrt{2}$.

Find the Slope of the Polar Curve at the Indicated r=6(1+cos⁡θ),θ=π4r = 6 ( 1 + \cos \theta ) , \theta = \frac { \pi } { 4 }r=6(1+cosθ),θ=4π​

Find the Slope of the Polar Curve at the Indicated $r = 6 ( 1 + \cos \theta ) , \theta = \frac { \pi } { 4 }$