Limit and Curve Intersections (Jee Mains)

Evaluation of Limits

Hard

Limit and Curve Intersections

Let f be a differentiable function on R such that f(2)= 1, f '(2) = 4. Let $\mathop {\lim }\limits_{x \to 0} {(f(2 + x))^{3/x}} = {e^\alpha }$ . Then the number of times the curve y = 4x³ – 4x² – 4(α – 7) x–α meets x-axis is :-

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