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Functions $f(x)$ and $g(x)$ are shown below:

$$f(x) = 3x^2 + 12x + 16,$$ $$g(x) = 2 \sin(2x - \pi) + 4$$

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

How do I find the minimum value? Can anyone show me?

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Hints: think derivative. Also, plot each. –  Amzoti Nov 7 '13 at 2:12
Have you tried to resolve it? You need to derive the function, set it equal to zero to find maximum and minimum. To sort can use the second derivative. –  Hiperion Nov 7 '13 at 2:16

1 Answer 1

You can solve it even without derivative.

about f: suppose $f(x)=3x^2+12x+16$ polynom from second degree (i.e in form of $ax^2+bx+c$). its minimum is located in $x_0=\frac{-b}{2a}$ and you can simply substitute.

about g: $\forall a\in\mathbb R,|\sin(a)|<1$, so in your function you're looking for an $x_1$ s.t $\sin(2x_1-\pi)=-1$.

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Actually the $x_0$ at the minimum is $x_0=-b/2a$ and then that value of $x$ should be plugged in. –  coffeemath Nov 7 '13 at 2:25
I fixed it. thanks. –  Coargu Aliquis Nov 7 '13 at 2:27
Yes. Now it looks good, and can be done with that approach by an algebra/trig student before learning calculus. Such courses usually cover the range of sine, cosine and the vertex of a parabola. (+1 for the simple accessible method). –  coffeemath Nov 7 '13 at 2:29

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