what are the inflection point relationship of stationary point and critical point what are the critical points f(θ)=sin⁡θcos2θ−cot⁡θθ+1 Domain:[0,2π]

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what are the inflection point  relationship of stationary point and critical point   what are the critical points  f(θ)=sin⁡θcos2θ−cot⁡θθ+1                Domain:[0,2π]

Alex Sheppard · Accepted Answer

What are inflection points?An inflection point is where the curve of the graph goes from concave down to up or vice versa. Point of inflection occur at f&#039;&#039;=0Relationship of stationary point and critical point. We say x0 is a stationary point of a function if f(x) and f&#039;(x) exist and is equal to f&#039;(x0)=0. And, x0 is a critical point of a function of f(x) if f(x0) exists and either f&#039;(x0) does not exist (i.e. function is not differentiable at or f&#039;(x0)=0.All stationary points are critical points but not all critical points are stationary points. What are the critical points?Point x0 is a critical point of a function of f(x) if f(x0) exists and either f&#039;(x0) does not exist (i.e. function is not differentiable at x0) or f&#039;(x0)=0.f(θ)=sin⁡θcos2θ−cot⁡θθ+1                Domain:[0,2π]The first derivative test is a method of analyzing functions using their first derivatives in order to find their extremum point. We take the derivative of the function,f′(θ)=ddθ(sin⁡θcos2θ−cot⁡θθ+1)=ddθ(sin⁡θcos2θ)−ddθ(cot⁡θθ)+ddθ(1)=cos3θ−−θcos⁡ec2θ−cot⁡θθ2−sin⁡2θsin⁡θNow,we substitute θ=4,f′(θ)=−0.27927−(−0.49047)−(−0.74875)=0.959951≈0.9600

what are the inflection point relationship of stationary point and critical

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