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A Game of X’s and O’s
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9
1
Determine the derivative of
each of the following
functions.
Answer for Square 1
1
a) 4ex/4
b) e(x^3 + x^2) x (3x2 + 2x)
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Determine the first and 2
second derivatives of the
following function.
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2
f´(x) = (7x6)(e(x^7))
+ 2xe(x^2)
f´´(x) = (42x5)(e(x^7))
+ (49x12)(e(x^7))
+ 2e(x^2)
+ (4x2)(e(x^2))
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Evaluate the
derivative of the
function at the
given value of x.
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f(x) = e^2x + e^(x^2)
at x = 2
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3
6e^4
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4
Determine the
derivative of each of
the following
functions:
a) y = 7^8x
b) y = 10 ^ ((x-1)^2)
a) y = 6 ^ ((x^2) + x – 2)
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a) y´ = 8ln7(7^8x)
b) y´ = (2x-2)(ln10)(10^((x-1)^2)
c) y´ = (2x+1)(ln6)(6^((x^2) + x – 2)
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5
5
Determine the
equation of the line
tangent to the
function at the given
value of x.
f(x) = (2x)(4^(x^2)) at x=1
5
f(x) = (8+16ln4)x – 16ln4
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6
6
Find a value of t such
that f´(t)=0, if it exists.
f(t) =
8t
2te^
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t = -1/8
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Answer for Square 6
7
A radioactive substance
decays exponentially over
time. The amount of the
substance that remains, P,
after t years is given by
P(t) = 100e-5t, where P is given
as a percent.
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a) Determine the equation of the rate of
change of the function
b) When 50% of the original sample has
decayed, what is the rate of decay ?
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a) P´(t) = -500e-5t
b) P´(1.059) = -2.5
7
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8
A drug is injected into the
body in such a way that the
concentration, C, in the
blood at time t hours is
given by the function
C(t) = 10e-2t - e-3t.
At what time does the
highest concentration occur
within the first 5h?
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During the first five
hours, the highest
concentration
occurs at about 0.41
hours.
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9
Given
f(x) = e-xcos2x,
find f’’(0).
is even.
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. Because
, then
is not even. Because
, then
is not odd. Therefore
is neither.
c)
. Therefore,
is even.
d)
. Therefore,
is even.
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Answer for Square 9