a so-called zero or solution is really just an x-intercept, in which case we set the dependent variable to 0, namely y = h(x) = 0 and solve for x to get it.
why is -3 the smallest? well, -3 is much smaller than 5 :), the further to the left you go on the number line, the smaller the number.
Answer:
45,54,63,72,81 for the 5 multiples of 9
63 is the least common multiple of 7 and 9
Step-by-step explanation:
Answer: We have
f'(x) = a x + b,
f'(x) = 0 at x = -b/a
f(x) = a x^2 / 2 + b x + c
Meaning of marked part
❟ ∵ a<0 ❟ f is a quadratic function
∴ f has absolute maximum value at x = -b/a
For all a with a less than zero, f is a quadratic function. Therefore f has a global maximum at x = -b/a
That typesetting seems very sloppy. It probably is supposed to be
∀a < 0, f is a quadratic function.
The second sentence is sloppy in use of "absolute". It can't mean absolute value, so presumably it means "global".
Sometimes a minimum or maximum is only local, but a quadratic function has exactly one extrema, and it is global. And if a < 0, the extrema is a global maximum.
Step-by-step explanation:
An extrema (minimum or maximum) for f(x) occurs only where f'(x) = 0, that is, when the slope of the tangent at x is zero.
But if the function crosses its tangent at that point, the point is an inflection point, not an extrema. A quadratic never crosses it's tangent.
<h2><u>
Answer:</u></h2>
Natalie has a total of <u>40 marbles.</u>
<u />
<h2><u>
Step-by-step explanation:</u></h2>
If 4 of Paiges' marbles are green, then we would write this as the ratio
<u>4:16</u>, or <u>1:4</u>
This means that for every green marble she has, she has 4 total marbles
Therefore, if Natalie has 10 green marbles, we would multiply this by 4 to get a total of <u>40 marbles.</u>