I need help on these problems THANK YOUUU
2 answers:
Answer:
2. m = 1
3. y - (-1) = 5 (x - 4)
4. y = 5x - 21
Step-by-step explanation:
<u>Work for #2</u>
m (slope) =
m =
m =
m = 1
<u>Work for #3</u>
y = -1/5x + 3 and through (4, -1)
The slope of a perperndicular line is the negative reciprocal. So, it is 5.
Plug this number into point-slope form. Use the points you were given (4,-1) in the equation as well.
y - y1 = m (x - x1)
y - (-1) = 5 (x - 4)
y + 1 = 5x - 20 (Only if you are supposed to simplify it)
<u>Work for #4</u>
Finish solving the equation
y - (-1) = 5 (x - 4)
y + 1 = 5x - 20
y = 5x - 20 - 1
y = 5x - 21
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Answer:
Step-by-step explanation:
The max and min values exist where the derivative of the function is equal to 0. So we find the derivative:
Setting this equal to 0 and solving for x gives you the 2 values
x = .352 and -3.464
Now we need to find where the function is increasing and decreasing. I teach ,my students to make a table. The interval "starts" at negative infinity and goes up to positive infinity. So the intervals are
-∞ < x < -3.464 -3.464 < x < .352 .352 < x < ∞
Now choose any value within the interval and evaluate the derivative at that value. I chose -5 for the first test number, 0 for the second, and 1 for the third. Evaluating the derivative at -5 gives you a positive number, so the function is increasing from negative infinity to -3.464. Evaluating the derivative at 0 gives you a negative number, so the function is decreasing from -3.464 to .352. Evaluating the derivative at 1 gives you a positive number, so the function is increasing from .352 to positive infinity. That means that there is a min at the x value of .352. I guess we could round that to the tenths place and use .4 as our x value. Plug .4 into the function to get the y value at the min point.
f(.4) = -48.0
So the relative min of the function is located at (.4, -48.0)