Calculus-derivatives

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Verify these answers~

1. For what value(s) of x does f(x)=(x^2-16)^5 have a horizontal tangent?

a) x=-4,4
b) x=-4,0,4
c) x=0
d) x=0,4

Answer is B, x=-4,0,4

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2. What is the derivative of f(x)=(3x^2+7)^3?

a) f'(x)=3(3x^2+7)^2

b) f'(x)=18(3x^2+7)^2

c) f'(x)=18x(3x^2+7)^2

d) f'(x)=3(3x^2+7)^2

Answer: C
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3. What is the y-intercept of the line that is tangent to f(x)=4/(3x+1) at (-1,-2)?

a) -5
b) -3/4
c) 3/4
d) -2

Answer: B
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4. For which point(s) on the graph of f(x)=5x/(x+2) is the slope of the tangent 2/5?

a) (-3,15)
b) (7, 35/9)
c) (3,3) and (-7,,7)
d) (24, 60/13)

Answer is C
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  • Calculus-derivatives -

    I am only going to do one of them. That should give you the idea.
    1. For what value(s) of x does f(x)=(x^2-16)^5 have a horizontal tangent?
    ---------------------------------
    when is dy/dx = 0?
    dy/dx = 5 (x^2-16)(2x)
    when is that zero
    When x = 0 obviously but also when
    x^2 = 16
    that is when x = 4 or x = -4
    so
    -4 , 0 , +4





    a) x=-4,4
    b) x=-4,0,4
    c) x=0
    d) x=0,4

    Answer is B, x=-4,0,4

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