What is the area of an isosceles right triangle whose hypotenuse is 5 √2 m long?
1 answer:
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Using limits, the polynomial that has an even degree and a negative leading coefficient is:
Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.
<h3>What is a limit?</h3>A limit is given by the value of function f(x) as x tends to a value.
In this problem, to find the polynomial, we have to find the limits as x goes to infinity, hence:
Since n is even, we have that:
Since it goes down to the left and down to the right, hence the function is:
Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.
More can be learned about limits at brainly.com/question/26270080
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The function increases in the interval (-∞, -3) and the function also increases in the interval (-1,∞) .
The given function is of the form
f(x) = x³ + 6x² + 8x
Now we take the first differentiation of the function
f'(x) = 2x² + 12x + 8
f'(x) = 2 (x² + 6x + 9) -10
f'(x) = 2(x+3)² - 10
Therefore at x = -3 , f'(x) = -10.
Hence the function is increasing in the interval of (-∞, -3)
Again f'(x) = 2x² + 12x + 8 , so after first differentiation we get :
That the function is also increasing in the interval (-1,∞)
Now for the interval (-4,-2), we can say that the graph of the function is positive as the y value increases and then decreases but all y values are positive as illustrated in the graph.
In the interval (0,∞) the function is strictly increasing and has positive values only.
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