For Exercises 132-135, use a graphing utility to a. Find the locations and values of the relative maxima and relative minima of the function on the standard viewing window. Round to 3 decimal places. b. Use interval notation to write the intervals over which f is increasing or decreasing. f x = − 0.4 x 3 − 1.1 x 2 + 2 x + 3
For Exercises 132-135, use a graphing utility to a. Find the locations and values of the relative maxima and relative minima of the function on the standard viewing window. Round to 3 decimal places. b. Use interval notation to write the intervals over which f is increasing or decreasing. f x = − 0.4 x 3 − 1.1 x 2 + 2 x + 3
Solution Summary: The author explains how the Ti-83 calculator determines the relative maxima and relative minima of the function.
a. Find the locations and values of the relative maxima and relative minima of the function on the standard viewing window. Round to 3 decimal places.
b. Use interval notation to write the intervals over which f is increasing or decreasing.
f
x
=
−
0.4
x
3
−
1.1
x
2
+
2
x
+
3
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
2. Find each derivative. Write answers with positive exponents.
a)
Dx 9x
-3
[97]
b) f'(3) if f(x) = x²-5x²
8
A ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related
rates questions below. (Hint: Use two carefully labeled similar right triangles.)
(a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt=
feet/sec.
(b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt=
feet/sec.
Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
Step 1
Using the diagram of a right triangle given below, the relation between x, y, and z is
z²
= x²+
+12
x
Step 2
We must find dz/dt. Differentiating both sides and simplifying gives us the following.
2z
dz
dt
dx
2x.
+2y
dt
dx
dy
dz
x
+y
dt
dt
dt
2z
dy
dt
×
dx
(x+y
dt
dy
dt
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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Grade 12 and UG/ Introduction to logical statements and truth tables; Author: Dr Trefor Bazett;https://www.youtube.com/watch?v=q2eyZZK-OIk;License: Standard YouTube License, CC-BY