Question

MEDAL!!!!!!!!!
Functions f(x) and g(x) are shown below:

Answer 1

f(x) = 3x2 + 12x + 16
g(x)

Answer 2

Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value

Answer 3

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)

Answer 4

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

Answer 5

For g(x) the minimum is at x = pi/2
so plug this into formula for g(x) to get the required minimum.

Answer 6

so f(x) isf '(x) = 6x + 12 =0 => x = -2

Answer 7

oh ok - you are using calculus
now plug -2 into f(x)

Answer 8

that equals 0

Answer 9

No - try again

Answer 10

its 4

Answer 11

what about g(x)

Answer 12

is that the smallest y value

Answer 13

yes g(x) is smallest minimum value

Answer 14

i get minimum value of g(x) = -2

Answer 15

g(x) = 2 sin (x - pi)
g'(x) = 2 cos ( x - pi) = 0 at turning points

Answer 16

explain how to find the minimum value for each function

Answer 17

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.

Answer 18

so for the first question f"(x) is 6 positive so thats a minimum

Answer 19

thanks for the help man

Answer 20

yw