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Math 131 WIR, copyright Angie Allen
Math 131 Week-in-Review #6 (Sections 3.2-3.4)
1. Find the derivative of each of the following functions. Do not simplify your answers.
a) f (x) =
√
x 2x2 − 4x + 7
(x3 − 7x + π 2)ex
b) f (x) = √
5
3 x3 − x4 + 2x − 3
rx2 + n
c) f (x) = m
+p
x
4
+ 3x − secx
x9
Math 131 WIR, copyright Angie Allen
d) f (θ ) =
2
3eθ + csc(θ )
+ 98θ cos(θ ) cot(θ )
1 + sin(θ )
2. Joe, a farmer in West Texas, is converting all of his crops to cotton. It is not feasible for him to convert all of his crops
to cotton at once. He is currently farming 400 acres of cotton this year and plans to increase that number by 70 acres
per year. As he becomes more experienced growing cotton, his output increases. He currently yields an average of 600
pounds of cotton per acre, but this average yield is increasing by 50 pounds per acre per year. How rapidly is the total
number of pounds of cotton increasing per year?
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Math 131 WIR, copyright Angie Allen
3. F and G are the functions whose graphs are shown below. (Source: #46, pg. 189, Stewart)
a) If P(x) = F(x)G(x), find P ′ (2).
b) If Q(x) = F(x)/G(x), find Q ′ (7).
4. Find equations of the tangent lines to the curve y =
Stewart)
c) If R(x) = G(F(x)), find R ′ (7).
x−1
that are parallel to the line x − 2y = 2. (Source: #54, pg. 190,
x+1
Math 131 WIR, copyright Angie Allen
5. Find the derivative of each of the following functions. Do not simplify your answers.
csc(2π x − 2)
a) f (x) = √
4
3x2 − 5x − 8
b) g(x) =
q
3
4
(5x2 e6x )2
c) h(x) =
sec(2π + tan(2π x))
√
2
7sin x x3 + 4x
4
Math 131 WIR, copyright Angie Allen
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d) k(θ ) = cot2 (sin(sin θ ))
6. Using calculus, determine where f (x) = x3 ex is increasing.
7. Find the equation of the line tangent to the curve y = tan(x) at x = π /3. Hint: sec x =
and cos(π /3) = 21 .
√
3
1
sin x
cos x , tan x = cos x , sin(π /3) = 2 ,
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Math 131 WIR, copyright Angie Allen
8. If r(k) = 3ek and k(a) = a2 − 5a + 3, find
9.
d
4x2 cos x cot x .
dx
dr
.
da