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Limits Continuity and Differentiability question

2025 · 4 Apr · Shift 2 · Q45

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Mathematics
Limits Continuity and Differentiability
2025 · 4 Apr · Shift 2 · Q45

Limits Continuity and Differentiability question

2025 · 4 Apr · Shift 2 · Q45

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f

be a differentiable function on

\mathbf{R}

such that

f(2)=1, f^{\prime}(2)=4

. Let

\lim \limits_{x \rightarrow 0}(f(2+x))^{3 / x}=\mathrm{e}^\alpha

. Then the number of times the curve

y=4 x^3-4 x^2-4(\alpha-7) x-\alpha

meets

x

-axis is :

A
3
B
1
C
2
D
0

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