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Show that the function f (x)={ {:(3x^...

Show that the function
`f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 ),(" "37 - x," "2 lt x le 3 ):}` is continuous at x = 2

A

f(x) is increasing on [-1, 2]

B

f(x) is continuous on [-1, 3]

C

f'(2) doesn't exist

D

f(x) has the maximum value at x = 2

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The correct Answer is:
A, B, D
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (More Than One Correct Option Type Questions)
  1. If f(x) = |x+1|(|x|+|x-1|), then at what point(s) is the function not ...

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  2. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

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  3. If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} th...

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  4. f(x) = cos x and H(x) = {{:(min{f(t), 0 le t lt x},0 le x le (pi)/(2))...

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  5. If f(x) = 3(2x + 3)^(2//3) + 2x + 3, then: (a) f(x) is continuous but ...

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  6. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

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  7. if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} ...

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  8. Let [x] denote the greatest integer less that or equal to x. If f(x) =...

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  9. The function f(x)=x-[x] , where [⋅] denotes the greatest integer fu...

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  10. The function f(x)=sqrt(1-sqrt(1-x^2)) a. has its domain -1 le x le 1 ...

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  11. Consider the function f(x) = |x^(3) + 1|. Then,

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  12. f is a continuous function in [a,b]; g is a continuous function in [b,...

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  13. Which of the following function(s) has/have the same range ?

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  14. If f(x) = sec 2x + cosec 2x, then f(x) is discontinuous at all points ...

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  15. Show that f(x)={{:("x sin"(1)/(x)",","when",x ne 0),(0",","when",x = 0...

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  16. A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0)...

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  17. Let f(x) = int(-2)^(x)|t + 1|dt, then a. f(x) is continuous in [-1, ...

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  18. A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y),...

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  19. Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 )...

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  20. If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x...

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