Let \( f(x) \) be differentiable function on the interval \( (-\infty, \infty) \) such that \( f... VIDEO
Let \( f(x) \) be differentiable function on the interval \( (-\infty, \infty) \) such that \( f(1)=5 \) and \( \lim _{a \rightarrow x} \frac{a f(x)-x f(a)}{a-x}=2 \), for all \( x \in R \) Then, which of the following alternative(s) is/are correct?
(a) \( f(x) \) has an inflection point
(b) \( f^{\prime}(x)=3, \forall x \in R \)
(c) \( \int_{0}^{2} f(x) d x=10 \)
(d) Area bounded by \( f(x) \) with coordinate axes is \( (2 / 3) \)
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