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Limits Continuity and Differentiability question

2020 · Shift 2 · Q27

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JEE Advanced
Mathematics
Limits Continuity and Differentiability
2020 · Shift 2 · Q27

Limits Continuity and Differentiability question

2020 · Shift 2 · Q27

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −2

Let f : R

\to

R and g : R

\to

R be functions satisfying f(x + y) = f(x) + f(y) + f(x)f(y) and f(x) = xg(x) for all x, y

\in

R. If

\mathop {\lim }\limits_{x \to 0} g(x) = 1

, then which of the following statements is/are TRUE?

A
f is differentiable at every x $\in$ R
B
If g(0) = 1, then g is differentiable at every x $\in$ R
C
The derivative f'(1) is equal to 1
D
The derivative f'(0) is equal to 1

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