The tangent to the curve y = e^3x at the point (0, 1), meets the x–ax…

The correct answer is Option (3) → \(\left(-\displaystyle\frac{1}{3}, 0\right)\)

The slope of the tangent is the value of \(\frac{dy}{dx}\) at the point:

    \(\frac{dy}{dx} = 3e^{3x}\)
    \(\text{at } x = 0: \ m = 3e^0 = 3\)

Equation of the tangent through (0, 1):

    \(y - 1 = 3(x - 0)\)
    \(y = 3x + 1\)

It meets the x-axis where y = 0:

    \(0 = 3x + 1\)

    \( \displaystyle x = -\frac{1}{3} \)

So the tangent meets the x-axis at \(\left(-\frac{1}{3}, 0\right)\).

Note: This topic was not in the CUET 2026 syllabus.