Derivatives
x2 + 2x - 4
2x + 2
e2x
2e2x
f(t) = 700 - 11t2 represents the height of a sand dune in feet at a given time t (years).
What is the height of the dune initially?
When does the height of the dune reach 0?
*Include units*
f(0) = 700 ft
t (when f = 0) = 7.977 years
sqrt(x4 + 2)
(2x3) / sqrt(x4 + 2)
ln(7x2 + pi)
(14x) / (7x2 + pi)
Given the equation for the position of an object at a given time t:
x(t) = t4 - 7t3 + (2/3)t - 2
Find the equations for velocity and acceleration in terms of time (v(t) and a(t)).
v(t) = 4t3 - 21t2 + (2/3)
a(t) = 12t2 - 42t
(x4 - 3x)(x + 4)2
(4x3 - 3)(x + 4)2 + 2(x4 - 3x)(x + 4)
2eln(e^(x^2))
4xe(x^2)
Write the equation for the population of a bacteria colony using P(t) = P0ert. Use t in terms of days.
The colony starts with 1000 bacteria and doubles in a day.
P(t) = 1000eln(2)t
(x2 + 2) / (3x)
(2x(3x) - 3(x2 + 3)) / (3x)2
ln((6x) / (3x2))
-1/x
Find the rate at which water drains from a tank holding 2000 gallons at t = 3 minutes if the equation for volume at a given time (minutes) is:
V(t) = 2000(1 - (t/20))2
*Include units*
V'(3) = -170 gallons/min
((17x) / 4) * sqrt((x3 + 2)3)
(17/4)sqrt((x3 + 2)3) + ((17x) / 4) * (3/2)sqrt(x3 + 2)(3x2)
esqrt(x^2 + 2) * ln(sqrt(x))
(xesqrt(x^2 + 2)ln(sqrt(x))) / (sqrt(x2 + 2)) + esqrt(x^2 + 2) / (2x)
Calculate the marginal profit of 60 units if:
R(x) = 0.3x2 - 24x
C(x) = 2500 - 22x
*Include Units*
P'(60) = $34