Functions and trig question, finding minimum value
1,402
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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Author by
emily
Updated on August 01, 2022Comments

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 yearsHints: think derivative. Also, plot each.

Hiperion almost 9 yearsHave 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 yearsActually the $x_0$ at the minimum is $x_0=b/2a$ and then that value of $x$ should be plugged in.

Admin almost 9 yearsI fixed it. thanks.

coffeemath almost 9 yearsYes. 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).