For Exercises 15-22, suppose that an object is attached to a horizontal spring subject to the given conditions. Find a model for the displacement d as a function of the time t . (See Example 1) Initial Displacement d at t = 0 Amplitude Period or Frequency 2.5 in . 2.5 in . 1.2 sec
For Exercises 15-22, suppose that an object is attached to a horizontal spring subject to the given conditions. Find a model for the displacement d as a function of the time t . (See Example 1) Initial Displacement d at t = 0 Amplitude Period or Frequency 2.5 in . 2.5 in . 1.2 sec
For Exercises 15-22, suppose that an object is attached to a horizontal spring subject to the given conditions. Find a model for the displacement
d
as a function of the time
t
. (See Example 1)
Initial Displacement
d
at
t
=
0
Amplitude
Period or Frequency
2.5
in
.
2.5
in
.
1.2
sec
Find all values of x for f (x)=(x²-4) 4 where the tangent line is horizontal.
5. Find the slope of the tangent line to the graph of f(x)=-√8x+1 at x=1. Write the equation of the tangent
line.
3. Find the derivative of each function. Label with appropriate derivative notation showing both dependent and
independent variables.
f(t)=4t(2t⭑+4)³
a. f(t)=4t (2t+4)³ (Answer must be factored.)
b.
y=
3
1
(2x³-4)
6
4.3 The Chain Rule
1. {Algebra review} Let f(x)=2x²-5 x and g(x)=6x+2. Find f[g(−5)].
2. {Algebra review} Write h(x)=√√8x-3 as the composite of two functions f(x) and g(x). (There may be more
than one way to do this.)
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