Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. f ( x ) = ( 2 x + 5 ) ( 3 x − 4 )
Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. f ( x ) = ( 2 x + 5 ) ( 3 x − 4 )
Solution Summary: The author explains how to calculate the derivative of the function, fprime (x), using product rule and then power rule.
Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results.
f
(
x
)
=
(
2
x
+
5
)
(
3
x
−
4
)
Formula Formula d d x f − g = d d x ( f ) − d d x ( g )
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
3. Solve the equation, give the answer exactly (no calculator approximations), and show all your
work. (4 points)
log5 2x = 3
Let I =
f(x) dx, where f is the function whose graph is shown.
4
2
y
f
X
1
2
3
4
(a) Use the graph to find L2, R2 and M2.
R₂
M2
=
=
=
(b) Are these underestimates or overestimates of I?
O 42 is an underestimate.
O 42 is an overestimate.
◇ R2 is an underestimate.
OR2 is an overestimate.
OM2 is an underestimate.
○ M2 is an overestimate.
(c) Use the graph to find T2.
T₂ =
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