I believe mohanrao with the respond/approach. even if, keep in mind that serious numbers are defined as places the place f '(x) =0 OR undefined. as an occasion, in case you had a rational functionality with an x on the denominator as f '(x), you're able to could desire to locate the place the numerator became equivalent to 0 AND state that x=0 is likewise a serious quantity (because of the fact something divided via 0 is undefined) whilst this concern does not have a concern the place f '(x) is undefined, it extremely is sturdy to keep in mind that -- f '(x) = undefined -- is a definition of a serious quantity.
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to find the critical points of a function, we need to find the first derivative and equal it to zero as the following:
f(x) = 2cos(θ) + (sin(θ))^2
f ' (x) = -2sin(θ) + 2sin(θ)cos(θ) ===>equal it to zero
0 = -2sin(θ) + 2sin(θ)cos(θ)
0 = -2sin(θ) [ 1 - cos(θ) ]
0 =-2sin(θ) =====> sin(θ) = 0 =====> θ = sin^-1 (0) =====> θ = 0 , π , & 2π ( critical points )
0 = 1 - cos(θ) =====> 1 = cos(θ) ====> θ = cos^-1 ( 0 ) ====> θ = 0 , π , 2π ( critical points )
I believe mohanrao with the respond/approach. even if, keep in mind that serious numbers are defined as places the place f '(x) =0 OR undefined. as an occasion, in case you had a rational functionality with an x on the denominator as f '(x), you're able to could desire to locate the place the numerator became equivalent to 0 AND state that x=0 is likewise a serious quantity (because of the fact something divided via 0 is undefined) whilst this concern does not have a concern the place f '(x) is undefined, it extremely is sturdy to keep in mind that -- f '(x) = undefined -- is a definition of a serious quantity.