Solve the equation. $x^2=100$
1 answer:
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The y-intercept of a function is that function's value when x=0.
.. f(0) = 4
.. g(0) = 0
These y-intercepts differ by 4.
If you want them to differ by zero (be the same), you have to move them to the same point.
Selection 1. Moves f(0) down 3 (to 1) and g(0) up 1 (to 1), so moves the y-intercepts to the same point. This is what you want, so this is an appropriate answer selection.
Selection 2. Moves f(0) up 4 (to 8) and g(0) down 1 (to -1). 8 and -1 are not the same point, so this is not the answer.
Selection 3. Moves f(0) down 2 (to 2) and g(0) up 1 (to 1). 2 and 1 are not the same point, so this is not the answer.
Selection 4. Moves f(0) up 3 (to 7) and g(0) down 6 (to -6). 7 and -6 are not the same point, so this is not the answer.
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The appropriate choice is the 1st one.
f(x) - 3 and
g(x) + 1
.. f(0) = 4
.. g(0) = 0
These y-intercepts differ by 4.
If you want them to differ by zero (be the same), you have to move them to the same point.
Selection 1. Moves f(0) down 3 (to 1) and g(0) up 1 (to 1), so moves the y-intercepts to the same point. This is what you want, so this is an appropriate answer selection.
Selection 2. Moves f(0) up 4 (to 8) and g(0) down 1 (to -1). 8 and -1 are not the same point, so this is not the answer.
Selection 3. Moves f(0) down 2 (to 2) and g(0) up 1 (to 1). 2 and 1 are not the same point, so this is not the answer.
Selection 4. Moves f(0) up 3 (to 7) and g(0) down 6 (to -6). 7 and -6 are not the same point, so this is not the answer.
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The appropriate choice is the 1st one.
f(x) - 3 and
g(x) + 1
For convenience sake, I will let
First, we evaluate the function at the endpoints of the interval.
Then, we need to find the critical points.
We can start by taking the derivative using the power rule.
Setting this equal to 0,
Since , we can divide both sides by
.
So, the absolute minimum is and the absolute minima are