What is the critical f(x)=5x^2sqrt(25-x^2) ?

The critical f(x)=5x^2sqrt(25-x^2) is x=-5,x=-(5sqrt(2))/(sqrt(3)),x=0,x=(5sqrt(2))/(sqrt(3)),x=5

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critical f(x)=5x^2sqrt(25-x^2)

critical points

f (x) = 5 x^{2} 25 - x^{2}

x = - 5, x = - \frac{5 2}{3}, x = 0, x = \frac{5 2}{3}, x = 5

Solution steps

5 x^{2} 25 - x^{2}

Find where

f^{'} (x)

is equal to zero or undefined

x = - \frac{5 2}{3}, x = 0, x = \frac{5 2}{3}, x = - 5, x = 5

Identify critical points not in

f (x)

domain

Domain of

5 x^{2} 25 - x^{2} : - 5 \leq x \leq 5

All critical points are in domain

x = - 5, x = - \frac{5 2}{3}, x = 0, x = \frac{5 2}{3}, x = 5

f (x) = \frac{1}{3} (x - 1)^{2} - 3

f (x) = \frac{x + 5}{x ^{2} + 9 x + 20}

f (x) = 2 \cdot x^{2} + x - 2

- (\frac{1}{3})^{x + 4}

f (x) = \frac{4 x - 3}{6 - 5 x}

What is the critical f(x)=5x^2sqrt(25-x^2) ?
The critical f(x)=5x^2sqrt(25-x^2) is x=-5,x=-(5sqrt(2))/(sqrt(3)),x=0,x=(5sqrt(2))/(sqrt(3)),x=5