anonymous
  • anonymous
MEDAL!!!!!!!!! Functions f(x) and g(x) are shown below:
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
f(x) = 3x2 + 12x + 16 g(x)
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anonymous
  • anonymous
Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value
welshfella
  • welshfella
for f(x) value of x at minimum is -b/2a ( that the a and b in the function ax^2 + bx + c) Then plug this into the formula for f(x) to get minimum value of f(x)

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anonymous
  • anonymous
g "(x) = -16sin(4x - π) > 0 for x = 5π/8, etc. So therefore, g(5π/8) = 2sin(π/4) + 4 = 4 + √2 > f(-2) = 4
welshfella
  • welshfella
For g(x) the minimum is at x = pi/2 so plug this into formula for g(x) to get the required minimum.
anonymous
  • anonymous
so f(x) isf '(x) = 6x + 12 =0 => x = -2
welshfella
  • welshfella
oh ok - you are using calculus now plug -2 into f(x)
anonymous
  • anonymous
that equals 0
welshfella
  • welshfella
No - try again
welshfella
  • welshfella
its 4
anonymous
  • anonymous
what about g(x)
anonymous
  • anonymous
is that the smallest y value
welshfella
  • welshfella
yes g(x) is smallest minimum value
welshfella
  • welshfella
i get minimum value of g(x) = -2
welshfella
  • welshfella
g(x) = 2 sin (x - pi) g'(x) = 2 cos ( x - pi) = 0 at turning points
anonymous
  • anonymous
explain how to find the minimum value for each function
welshfella
  • welshfella
using calculus you find the first derivative and equate it to zero and solve for x this will give you a critical point you can now test for maximum or minimum by taking the second derivative and finding its sign for the value of x you have found positive value is minimum and negative is a maximum.
welshfella
  • welshfella
so for the first question f"(x) is 6 positive so thats a minimum
anonymous
  • anonymous
thanks for the help man
welshfella
  • welshfella
yw

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