Answer : Option D is correct i.e [2.5,4]
Explanation :
Suppose our function is f(x)
then the value of f(x) is minimum where
it reaches -0.44 and 3 with two different intervals .
As we know that for finding the local minimum ,
the criteria is that f'(x)=0 .
So, here
f'(-0.44)=0 and
f'(3)=0
both are the local minimum point for the function f(x)
but -0.44 is the global minimum point .
In our case for [2.5,4] is the required interval where f(x) reaches its local minimum.
We can use trigonometry. The cosine of 15 will be the side adjacent to the 15-degree side (the one we are looking for) divided by 20, the hypotenuse. As cos(15) is about .966, we get 19.32 as the side we are looking for.
One application of volume is determining the density of an object. Assume the object is made of a pure element (eg: gold). If we know the volume (v) of the object, and we know the mass (m), then we can use the formula D = m/v to figure out the density D. Knowing the volume is also handy to determine if the object can fit into a larger space or not. Another application is figuring out how much water is needed to fill up the inner space of the 3D solid (assuming it's hollow on the inside).
The surface area is handy to figure out how much material is needed to cover the outer surface. This material can be paint, paper, metal sheets, or whatever you can think of really. A good example is wrapping a present and the assumption is that there is no overlap.
