The number of points of local maxima of the function $f(x) = x + \sin x$ is-

Find the maximum area of an isosceles triangle inscribed in the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with its vertex at one end of the major axis.

$A$ wire of length $20 \ m$ is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in $meters$) of the hexagon,so that the combined area of the square and the hexagon is minimum,is:

$A$ square piece of tin of side $18 \, cm$ is to be made into a box without a top by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible (in $, cm$)?

In the interval $[0, 2\pi]$,the slope of the tangent to the function $f(x) = e^x \sin x$ is maximum at $x = \dots$

In the interval $(-4, 4)$,the function $f(x) = \int_{-10}^x (t^4 - 4)e^{-4t} dt$ has: