Page 61 - How To Solve Word Problems In Calculus

dx
Since = 3,
dt
dy
2
= (3x + 8x) · 3
dt
dx dy
Even though is constant, changes as x changes. When
dt dt
x = 1
dy
= 11 · 3 = 33
dt
In solving word problems, the following steps should be
followed:

Step1
Draw a diagram (if applicable). Label all variables with
an appropriate symbol. Label constants with their numer-
ical values.

Step2
Determine which rates are given and which rate you
need to find. Write them down for future reference.

Step3
Find an equation (or several equations) relating the vari-
ables defined in step 1.
Step4
Differentiate the equation(s) in step 3 with respect to
time.

Step5
Substitute all given information into the result of step 4
and solve for the unknown rate. Insert appropriate units.

The basic technique is illustrated in the next example.
EXAMPLE 4
A ladder 20 feet long is placed against a wall. The foot of the
ladder begins to slide away from the wall at the rate of 1 ft/sec.
How fast is the top of the ladder sliding down the wall when
the foot of the ladder is 12 feet from the wall?

48