The function, f(x)=(3x-7)x2/3,x∈R is increasing for all x lying in:

f(x)=(3x-7)x2/3f'(x)>0⇒x2/315x-143x>0⇒x(15x-14)>0 f increases for all n∈(-∞,0)∪1415,∞

The function, f(x)=(3x-7)x2/3,x∈R is increasing for all x lying in:

f(x)=(3x-7)x2/3f'(x)>0⇒x2/315x-143x>0⇒x(15x-14)>0 f increases for all n∈(-∞,0)∪1415,∞

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$The function, f (x) = (3 x - 7) x^{2 / 3}, x \in R is increasing for all x lying in:$

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$(- \infty, \frac{14}{15}) \cup (0, \infty)$

$(- \infty, \frac{14}{15})$

$(- \infty, 0) \cup (\frac{14}{15}, \infty)$

$(- \infty, 0) \cup (\frac{3}{7}, \infty)$

answer is C.

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$\begin{array}{l} f (x) = (3 x - 7) x^{2 / 3} \\ f^{'} (x) > 0 \Rightarrow x^{2 / 3} (\frac{15 x - 14}{3 x}) > 0 \\ \Rightarrow x (15 x - 14) > 0 \\ f increases for all n \in (- \infty, 0) \cup (\frac{14}{15}, \infty) \end{array}$

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The function, f(x)=(3x-7)x2/3,x∈R is increasing for all x lying in:

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$The function, f (x) = (3 x - 7) x^{2 / 3}, x \in R is increasing for all x lying in:$