MCQ
The interval for which the given function $f(x) = 2{x^3} - 3{x^2} - 36x + 7$ is decreasing, is
- ✓$(-2, 3)$
- B$(2, 3)$
- C$(2,-3)$
- DNone of these
$ \Rightarrow f'(x) = 6{x^2} - 6x - 36$ but for decreasing $f'(x) < 0$
==> ${x^2} - x - 6 < 0 \Rightarrow (x - 3)(x + 2) < 0$ ==> $ - 2 < x < 3$
Hence the required interval is $ (-2, 3).$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$f(x)\, = \left\{ {\begin{array}{*{20}{c}}{x\,\sin \,\left( {\frac{1}{x}}\right)\,\,\,\,\,\,\,for\,\, - 1 \le x \le 1\,\,and\,\,x \ne \,0}\\
{0\,\,\,\,\,\,\,\,\,\,\,\,for\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, = \,0}
\end{array}} \right.$
$g(x)\, = \left\{ {\begin{array}{*{20}{c}}{{x^2}\,\sin \,\left( {\frac{1}{x}} \right)\,\,\,\,\,\,\,for\,\, - 1 \le x \le 1\,\,and\,\,x \ne \,0}\\{0\,\,\,\,\,\,\,\,\,\,\,\,for\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, = \,0}\end{array}} \right.$ $h (x) = | x |^3$ for $- 1 \le x \le 1$ Which of these functions are differentiable at $x = 0$ ?