Let f be a differentiable function on ℝ such that f(2) = 1 and f'… | JEE Main 2025 Mathematics PYQ

MCQHardJEE Main 2025 · 4 April, Shift 2Derivatives of Functions

Let $f$ be a differentiable function on $\mathbb{R}$ such that $f(2) = 1$ and $f'(2) = 4$ . Let $\lim_{x \to 0} \left( f(2+x) \right)^{3/x} = e^\alpha$ . Then the number of times the curve $y = 4x^3 - 4x^2 - 4(\alpha - 7)x - \alpha$ meets the x-axis is:

A
$2$
B
$1$
C
$0$
D
$3$

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