Example 11
Find the critical points of f (x) = 2x^{4}
 32x2
Solution : Since f (x) is a polynomial in x, x Î
R.
Now f ' (x) = 8x^{3}  64x
\ For
critical points, f ' (x) = 0 Þ
8x^{3}  64x = 0
8x (x^{2}  8) = 0
Example 12
Find all critical points of f (x) = sin x + cos x on [0 , 2 p]
Solution : Given that for f (x) = sin x + cos x , x Î
[0, 2 p]
Now f ' ( x ) = cos x  sin
x
for critical
points, f ' ( x ) = 0 Þ cos
x  sin x = 0
\ cos
x = sin x Þ tan
x = p/4
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