極值問題，請問圈起來的題目怎麼解?

臨界點 ( critical point ) 包含以下三種:
(1) 端點
(2) 奇異點 ( singular point ) , 即 f ' (x) 不存在之點.
(3) 平穩點 ( stationary point ) , 即滿足 f ' (x) = 0 之點.

10.
h(x) = sin^2 x + cos x , 0 < x < 2π
(1) 有兩個端點在 x = 0 , 2π
(2) h' (x) = 2*sin x*cos x - sin x , 導函數在定義域 ( 0 , 2π ) 皆存在, 故無奇異點.
(3)
h' (x) = sin x*( 2cos x - 1 ) = 0
sin x = 0 或 cos x = 1/2
故平穩點在 x = π , π/3 , 5π/3
綜合以上, 臨界點在 x = 0 , π , π/3 , 5π/3 , 2π
Ans: x = 0 , π , π/3 , 5π/3 , 2π

14.
f(x) = x^2 * log(底數2)(x^2+1)
(1) 無端點
(2)
f ' (x)
= 2x*log(底數2)(x^2+1) + x^2*[ 1 / (x^2+1) ]*( 1 / ln 2 )*( 2x )
= 2x*ln(x^2+1)/ln 2 + 2x^3/[ (x^2+1) * ln 2 ]
= ( 2x / ln 2 )*[ ln(x^2+1) + x^2/(x^2+1) ]
導函數皆存在, 故無奇異點.
(3)
f ' (x) = ( 2x / ln 2 )*[ ln(x^2+1) + x^2/(x^2+1) ] = 0
x = 0 或 ln(x^2+1) = - x^2/(x^2+1)
ln(x^2+1) ≧ ln 1 = 0
- x^2/(x^2+1) ≦ 0
所以只有 x = 0 可滿足 ln(x^2+1) = - x^2/(x^2+1)
故平穩點在 x = 0
綜合以上, 臨界點在 x = 0
Ans: x = 0