If f ( x )=5 x x 3 , find a l l critical numbers of f ( x ). 2. For the function

Question

If f(x)=5xx      3   , find all critical numbers of f(x).

2.

For the function f(x)=sin 2 x , find the absolute maximum value M and the absolute minimum value m on the interval [0,23 ].

If f(x)=5xx      3   , find all critical numbers of f(x).

A) x=52 ,5 only


B) x=0,5 only


C) x=0 only


D) x=0,52 ,5


E) x=5 only

2.

For the function f(x)=sin 2 x , find the absolute maximum value M and the absolute minimum value m on the interval [0,23 ].

A) m=1,  M=34  


B) m=12 ,  M=1


C) m=0,  M=34  


D) m=0,  M=1


E) m=0,  M=3   2  

Explanation / Answer

f(x) = sin2x ; f'(x) = 2cos2x ;

2cos2x =0 -----> cos2x=0 in the interval [0,2pi/3]

x = pi/4

Now evaluatin x = 0, pi/4 , 3pi/2

f(0) =0 and f(pi/4) = 1 and f(3pi/2) =0

So, maxima M =1 and minima m=0

Option D

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