1. The side of a cube increases at the rate of 12 m/sec. Find the rate at which the volume of the cube increases when the side of the cube is 5 m.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
1. The side of a cube increases at the rate of 12
m/sec. Find the rate at which the volume of
the cube increases when the side of the
cube is 5 m.
2. The radius of a sphere decreases at the rate
of 1 m/sec. Find the rate at which the
volume decreases when the radius is 2 m.
3. Find the absolute extremum values of
f(x) = x² – 4x + 24 over the interval [1, 4]
-
4. Check whether the Mean Value Theorem can
be applied to the function
f(x) = 2x? – 9x + 7 defined over the
interval [1,6]. Justify your answer.
-
Transcribed Image Text:1. The side of a cube increases at the rate of 12 m/sec. Find the rate at which the volume of the cube increases when the side of the cube is 5 m. 2. The radius of a sphere decreases at the rate of 1 m/sec. Find the rate at which the volume decreases when the radius is 2 m. 3. Find the absolute extremum values of f(x) = x² – 4x + 24 over the interval [1, 4] - 4. Check whether the Mean Value Theorem can be applied to the function f(x) = 2x? – 9x + 7 defined over the interval [1,6]. Justify your answer. -
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