The correct structure of the question is as follows:
The function f(x) = x^3 describes a cube's volume, f(x) in cubic inches, whose length, width, and height each measures x inches. If x is changing, find the (instantaneous) rate of change of the volume with respect to x at the moment when x = 3 inches.
Answer:
Step-by-step explanation:
Given that:
f(x) = x^3
Then;
V = x^3
The rate whereby V is changing with respect to time is can be determined by taking the differentiation of V
dV/dx = 3x^2
Now, at the moment when x = 3;
dV/dx = 3(3)^2
dV/dx = 3(9)
dV/dx = 27 cubic inch per inch
Suppose it is at the moment when x = 9
Then;
dV/dx = 3(9)^2
dV/dx = 3(81)
dV/dx = 243 cubic inch per inch
Answer:
neither
Step-by-step explanation:
they are parallel when they have the same slope and perpendicular when the slope is completely different
Answer: (B) 3 times as fast
<u>Step-by-step explanation:</u>
rate of change is the "slope" between the given interval.
f(x) = 125(.9)ˣ
f(1) = 125(.9)¹
= 112.5
f(5) = 125(.9)⁵
= 73.8
********************
f(11) = 125(.9)¹¹
= 39.2
f(15) = 125(.9)¹⁵
= 25.7
********************
The rate of change from years 1 to 5 is approximately 3 times the rate of change from years 11 to 15.
