If at a point on the curve y = f(x) the slope of the line tangent to the curve is equal to 2xy , then the function f is: - Mathematics MCQ Mathematics Mock Test - 5 2026 | ExamTest.live

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If at a point on the curve y = f (x) the slope of the line tangent to the curve is equal to 2 x y, then the function f is:

Solution & Step-by-step Explanation

The slope of the tangent is \frac{d y}{d x} .Given: \frac{d y}{d x} = 2 x y Separating variables: \frac{1}{y} d y = 2 x d x Integrating both sides: \int \frac{1}{y} d y = \int 2 x d x ln y = x^{2} + C y = e^{x^{2} + C} y = e^{C} \cdot e^{x^{2}} This is an exponential function.

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If at a point on the curve y = f (x) the slope of the line tangent to the curve is equal to 2 x y, then the function f is:

Linear

Logarithmic

Exponential

Trigonometric

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