Find all relative extrema of the function. use the second derivative test where applicable. (if an answer does not exist, enter dne.) f(x) = x3 − 9x2 + 2

Answers

Answer 1

Answer: First find the derivative of the function. The derivative is $f'(x)=3 x^(2) -18x$ . Now set it equal to 0 to find the critical numbers. $0=3 x^(2) -18x$ . Factor to solve for the zeros of the derivative. $0=3x(x-6)$ . So 3x = 0, and x = 0, or x - 6 = 0 and x = 6. We will make a table with values for -∞<x<0, 0<x<6, 6<x<∞. Pick a value within those boundaries for each interval and find the sign, positive or negative, that results from subbing that number into the derivative. If we choose -1 in the first interval f'(-1)=21, so the function is increasing from negative infinity to 0. If we choose 1 in the second interval, f'(1)=-15, so the function is decreasing from 0 to 6. If we choose 10 in the last interval, f'(10)=120, so the function is increasing from 6 to infinity. The points of extrema are found by subbing the critical x values into the original function. We know the function is increasing from negative infinity to 0, so f(0)=2, and our max point is (0, 2). We know the function is decreasing from 6 to infinity, so f(6)=-106, and our min point is (6, -106). I do this instead of the second derivative test, but they both work.

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Answers

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(6+6+6)(36+1) = (18)(37) = 666. ... If you don't want an answer posted, there's a simple solution ... don't post the question ! And if it still mysterously somehow appears, then for heaven's sake, don't offer points as a reward for an answer. ... Finally ... devil's numbers belong in the Old Wives' Hooey category, not in the Mathematics one. They're not real.

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Answer:

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Step-by-step explanation:

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The answer for the y intercept is (0,4)

If you're plotting the value of f(x) on the y-axis,
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Answer:

Step-by-step explanation:

Answer:

Is A

Step-by-step explanation:

Solve the equation -1/3m-7=5

Answers

The Equation:    -1/3 m - 7 = 5

Please watch me closely.

Add 7 to each side:    -1/3 m = 12

Multiply each side by 3 : -1 m = 36

Multiply each side by -1 :    m    = -36

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