part 1 of 1 - question 15 of 50 2 points find the equation of the normal line to the graph of h(x)=5 cos x +…

Explanation:

Step1: Find the derivative of $h(x)$

$h(x)=5\cos x + 5\sin x$, so $h^\prime(x)=- 5\sin x+5\cos x$.

Step2: Evaluate the derivative at $x = \frac{\pi}{2}$

$h^\prime(\frac{\pi}{2})=-5\sin\frac{\pi}{2}+5\cos\frac{\pi}{2}=-5\times1 + 5\times0=-5$.

Step3: Find the slope of the normal line

The slope of the normal line $m$ is the negative - reciprocal of the slope of the tangent line. Since the slope of the tangent line at $x=\frac{\pi}{2}$ is $-5$, then $m=\frac{1}{5}$.

Step4: Use the point - slope form to find the equation of the normal line

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(\frac{\pi}{2},5)$ and $m = \frac{1}{5}$. So $y-5=\frac{1}{5}(x - \frac{\pi}{2})$, which can be rewritten as $y = 5+\frac{1}{5}(x-\frac{\pi}{2})$.

Answer:

B. $y = 5+\frac{1}{5}(x-\frac{\pi}{2})$