1.

If f(x)={:{(3x^2+12"," x-1),(37-x ","2 lt x le 3):} then

Answer»

f(X) INCREASING on [-1,2]
f(x) is continuos on [-1,3]
f(2) does not exist
all of these

Solution :`underset(xrarr2^-)limf(x)=underset(xrarr2^+)limf(x)=f(2)`
So f(x) is CONTINUOUS on [-1,3] THUS options (b) and (c ) are correct .
ALSO
`(LHD at x =2) ={d/(dx)(37 -x)}_(atx=2)`=24
Clearly f(x) is not differentiableat x=2
So f(2) does not exist.
Now `f(x)={(6x+12","-1 lt xlt 2 ),(-1","2 ltx lt 3):}`
Cleary `f' (x)lt 0 for all x in [-1, 2] `
So f(x) in increasing on [-1,2]
Thus option (a) is correct .


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