List of top Mathematics Questions on Application of derivatives asked in MET

The least value of \(a\), for which the function \[ \frac{4}{\sin x} + \frac{1}{1-\sin x} = a \] has at least one solution in the interval \(\left(0,\frac{\pi}{2}\right)\), is:

The curve, for which the area of the triangle formed by X-axis, the tangent line at any point \(P\) and line \(OP\) is equal to \(a^2\), is given by

By Newton-Raphson method, the positive root of \(x^4 - x - 10 = 0\) is:

If \(2a + 3b + 6c = 0\), then the equation \(ax^2 + bx + c = 0\) has at least one real root in

The value of \(\lim_{n \to \infty} \left\{\frac{1}{na} + \frac{1}{na+1} + \frac{1}{na+2} + \ldots + \frac{1}{nb}\right\}\) is

The two curves \( x^3 - 3xy^2 + 2 = 0 \) and \( 3x^2y - y^3 = 2 \) are

The slope of the tangent to the curve \( y = x^{2 - x} \) at the point where \( x = 2 \) is:

The slope of the tangent to the curve $y = x^{2 - x$ at the point where $x = 2$ is: