If the area under the curve of f(x) = 25 - x^2 from x = -4 to x = 0 is estimated using four approximating rectangles and left endpoints, will the estimate be an underestimate or overestimate?

Question

1) Underestimate

2) Overestimate

3) The area will be exact

Answer 1

GRAPH IT(0at x=-5, 9 at x=-4, 25 at x=0
dy/dx = -2 x
d^2y/dx^2 =-2
This curve curves down (sheds water, d^2y/dx^2 <0 ) while the slope is positive for negative x
Therefore those rectangles do not fill the space under the curve.

Answer 2

In the given region, the graph is moving downwards.

Left endpoint approximation does not cover the entire region, and will hence give an underestimate.

Answer 3

thank you

Answer 4

It is not moving downwards. It is curving downwards :)