Question

Determine for what numbers, if any, the given function is discontinuous.

f(x)=x-5 if x <=5
x^2-10 if x >5
A. 5
B. None
C. 0
D. -5, 5
The function f(x) = x3  describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. If x is changing, find the average rate of change of the volume with respect to x as x changes from 1 inches to 1.1 inches.

 A. 2.33 cubic inches per inch  B. -3.31 cubic inches per inch  C. 23.31 cubic inches per inch  D. 3.31 cubic inches per inch

please help

Answer 1

The answer of the first question is x=5 When, x=5, f(x)=0, if x➡ 5-, f(x)➡0 also. But when x➡ 5+,f(x)➡ 15. that's why f(x) is discontinuous in x=5, you can materialise it easily plotting a graph. And the answer of the third question is D, the change rate is [(1.1)³-1³]/0.1=3.31