Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

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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  • 4 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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