Application Of Derivatives - Calculus - Mathematics Previous Year Questions

The interval in which the function \(f(x)=\sin x-\cos x, 0 \leq x \leq 2 \pi\) is strictly decreasing, is

The slope of normal to the curve \(y=x^3+2 x+6\) which is parallel to line \(x+14 y+4=0\) is

The maximum slope of the curve \(y=\frac{1}{2} x^4-5 x^3+18 x^2-19 x\) occurs at the point

\(f\) and \(g\) are differentiable function in \((0,1)\) satisfying \(f(0)=2=g(\mathrm{l}), g(0)=0\) and \(f(l)=6\), then for some \(c \in] 0,1[\)

The maximum slope of the curve \(y=\frac{1}{2} x^4-5 x^3+18 x^2-19 x+7\) occurs at the point

Difference between the maximum and minimum values of $f(x)=-\sin ^3 x+3 \sin ^2 x+5$ in $x \in\left[0, \frac{\pi}{2}\right]$ is

If tangent to the curve $f(x)=x^3-\alpha x^2-x+\beta$ at point $(1,3)$ on the curve, cut equals non zero intercepts on co-ordinate axes, then

The length of three sides of a trapezium are equal, each being 10 cms . Then, the maximum area $\left(\mathrm{cm}^2\right)$ of the trapezium is