# Functions and trig question, finding minimum value

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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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### emily

Updated on August 01, 2022

• emily 3 months

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?

• Amzoti almost 9 years
Hints: think derivative. Also, plot each.
• Hiperion almost 9 years
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.
• coffeemath almost 9 years
Actually the $x_0$ at the minimum is $x_0=-b/2a$ and then that value of $x$ should be plugged in.