Question

find the critical points on the given interval
\[2^{x}\sin x; [-2,6]\]

Answer 1

Start by finding the derivative of the function

Answer 2

By definition, x=c is a critical point of the function if:

f"(c) = 0 or f'(c) = DNE

Answer 3

\[2^{x}\ln 2(\sin x) + 2^{x}\cos x\] right

Answer 4

Correct.

Answer 5

Now, apply the definition I just provided. Set your deriviative equal to zero.

Answer 6

well this is where i'm lost

Answer 7

Well, you can factor out:\[2^x(\cos(x)+\ln(2)\sin(x))\]\[2^x = 0, \cos(x)+\ln(2)\sin(x)=0\]

Answer 8

Does that make it a bit easier?

Answer 9

well i got that far but doesn't that still only leave 2 answers as to what x is

Answer 10

I think one answer is DNE.

Answer 11

book claims that it's -.96 , 2.18, 5.32