the function (f(x)=\frac{8}{sqrt{63}}x - arcsin(x)) has two critical values. determine these two critical…

the function (f(x)=\frac{8}{sqrt{63}}x - arcsin(x)) has two critical values. determine these two critical values. enter the smaller critical value in the first blank and the larger critical value in the second blank. smaller critical value: larger critical value:

the function (f(x)=\frac{8}{sqrt{63}}x - arcsin(x)) has two critical values. determine these two critical values. enter the smaller critical value in the first blank and the larger critical value in the second blank. smaller critical value: larger critical value:

Answer

Explanation:

Step1: Find the derivative of the function

The function is (y = \frac{8}{\sqrt{63}}x-\arcsin(x)). The derivative (y'=\frac{8}{\sqrt{63}}-\frac{1}{\sqrt{1 - x^{2}}}) (using the derivative formulas (\frac{d}{dx}(ax)=a) and (\frac{d}{dx}(\arcsin(x))=\frac{1}{\sqrt{1 - x^{2}}})).

Step2: Set the derivative equal to zero

Set (\frac{8}{\sqrt{63}}-\frac{1}{\sqrt{1 - x^{2}}}=0). Then (\frac{1}{\sqrt{1 - x^{2}}}=\frac{8}{\sqrt{63}}), cross - multiply to get (\sqrt{63}=8\sqrt{1 - x^{2}}). Square both sides: (63 = 64(1 - x^{2})). Expand: (63=64 - 64x^{2}). Rearrange to find (64x^{2}=1), so (x^{2}=\frac{1}{64}), and (x=\pm\frac{1}{8}).

Answer:

Smaller Critical Value: (-\frac{1}{8}) Larger Critical Value: (\frac{1}{8})