Question

HELP PLEASE!
Find the points of inflection of the graph of the function. (If an answer does not exist, enter DNE.)
f(x) = 5 sin x + 5 cos x, [0, 2π]
(x, y) = (smaller x-value)
(x, y) = (larger x-value)


Describe the concavity. (Enter your answers using interval notation.)
concave upward :
concave downward :

Answer 1

Well you know what gives us points of inflection correct?

Answer 2

no i don't @hilbertboy96

Answer 3

ik i have to take the second derivative which would be -5 sin(x)-5cos(x), and set that to zero correct? that would be -5 sin(x)- 5cos(x)=0
then i have to factor out the 5? -5(sin(x)+cos(x))=0, but then i forget what to do next

Answer 4

\[ -5 \sin(x)- 5\cos(x)=0\]\[ \implies \sin(x)+\cos(x)=0\].... next can you rewrite this sum of two sinusoidal function as a single sine function?

Answer 5

sin(x)=0 ?

Answer 6

sorry nvm what i said earlier ...
\[ \sin(x)+\cos(x)=0\]\[\implies \sin(x)=-\cos(x)\]\[\implies \tan(x)=-1\]

Answer 7

ok, so do i plug the -1 into the original function?

Answer 8

@PaxPolaris

Answer 9

no you need to solve for x still ...

Answer 10

for x from the original function or the one above?

Answer 11

in the domain: \(0\le x \le 2\pi\)\[\tan (x)=-1\]\[\implies x={3\pi \over4}\text { OR } x={7\pi \over4}\]

Answer 12

ok, so i would use those and substitute that for x in the original function?

Answer 13

right, to get y for the 2 inflection points

Answer 14

ok, thanks