Question
If f(x)= \ array cc x^2 ( x) (1+x) , & x 0 \\ 0, & x=0 array ., then at x=0, f(x) is
BITSAT
Mathematics
Continuity and Differentiability
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. not continuous
- B. continuous but not differentiable
- C. differentiable
- D. not continuous, but differentiable
Answer
C. differentiable
Step-by-step solution
_ x 0 f(x)= _ x 0 x^2 ( x) (1+x) = _ x 0 - x ( x) (1+x) x = _ x 0 x ( x)=0 1=0 _ x 0 f(x)=f(0) f(x) is continuous at x=0 Now, _ x 0 f(x+h)-f(x) h _ h 0 f(h)-f(0) h = _ h 0 h^2 h-0 (1+h) _ h 0 h^2 ( h) 1 =0 f(x) is differentiable at x=0
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