Solving for zero using differentiation

Question

I need help finding the min and max to the equation $y'= 4.9385 \cos(0.017(x-80)).$ I've tried this by making $y' = 0$ and tried to solve for $x$ but I don't understand how to do it. So, can someone please help find the min and max for $0 = 4.9385 \cos(0.017(x-80))$ ?

Answer 1

Given the equation:

$$ y = A \sin( \kappa\, (x-a) ) $$

The min max of $y$ is $$ y' = A \kappa \cos(\kappa\, (x-a) ) =0$$

This is solved by $\cos(\kappa\, (x-a) )=0$ or

$$ \kappa\, (x-a) = \frac{\pi}{2} + n \pi $$

Answer 2

The min/max of $y$ is when $y'$ is 0. We solve this equation to find the min/max: $4.9385 \cos(0.017(x-80))=0 \implies 0.017(x-80)=90\text{ or }270\implies x = \frac{91360}{17}, \frac{271360}{17}$. The min and max are when $x = \frac{91360}{17}, \frac{271360}{17}$.