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# f(x)=5sinx+4cosx,on(−π,π) 1 critical point? 2 inflection points?

Update:

please I need the detail on how to find the critical point !!

Update 2:

All the angles which satisfy the derivative function on (-pi, pi) ????????????

is arctan(5/4) is the only value satisfy on (-pi, pi) ??????????????

Update 3:

All the angles which satisfy the derivative function d/dx=0 on (-pi, pi) ???

### 1 Answer

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- L. E. GantLv 74 weeks ago
f'(x) = 5cos(x) - 4sin(x)

critical points when f'(x) = 0

==> 4sin(x) = 5cos(X)

==> tan(x) = 5/4

==> x = arctan(5/4) or -π + arctan(5/4)

follow on update: tan is positive in the first quadrant (that's 0 to pi/2) and the third quadrant (that's -pi to - pi/2), and those are all the values from -pi to +pi

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