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Question

Let f(x)={ax,x<2ax2bx+3,x2
If f(x) is differentiable for all x, then
  1. a=34b=94
  2. a=32,b=92
  3. a=1,b=2
  4. a=34,b=114


Solution

The correct option is A a=34b=94

f(x) is differentiable  f(x) is continuous

f(x) is continuous at x = 2    2a = 4a - 2b + 3     2a - 2b + 3 = 0                      . . . .(1)

f(x) is differentiable at x = 2         a = 4a - b         3a - b = 0                                        . . . .(2)

solving (1) and (2), we have a=34,b=94

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