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3 years ago

Given the function f(x)=x^4+8x^3+16x^2, determine all intervals on which f is decreasing.

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

4 0

Answer:

see attachment

Step-by-step explanation:

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Answer:

step-by-step explanation:

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3 years ago

Ye is riding home from a friend's house. After 5 minutes he is 4 miles from home, after 15 minutes Ye is 2 miles from home. Whic

Ad libitum [116K]

Answer:

$y = -\frac{1}{5}x + 5$

Step-by-step explanation:

Given

$5\ minutes = 4\ miles$

$15\ minutes = 2\ miles$

Required

Determine the equation

y represents distance

x represents time

So, the given parameters can be modeled (x,y) as:

$(x_1,y_1) = (5,4)$

$(x_2,y_2) = (15,2)$

First, we need to determine the slope of the function.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{2 - 4}{15 - 5}$

$m = \frac{-2}{10}$

$m = -\frac{1}{5}$

The equation can be determined using:

$y - y_1 = m(x - x_1)$

Where

$m = -\frac{1}{5}$

$(x_1,y_1) = (5,4)$

$y - y_1 = m(x - x_1)$

becomes

$y - 4 = \frac{-1}{5}(x - 5)$

Open bracket

$y - 4 = -\frac{1}{5}x + 1$

Solve for y

$y = -\frac{1}{5}x + 1 + 4$

$y = -\frac{1}{5}x + 5$

7 0

3 years ago

Can someone explain to me how to do this?

elena55 [62]

In the slope intercept form equation of a line (y=ax+b) a represents the slope, and b represents the intercept, which is -5. Thus, we know y=ax-5. The slope can be found by creating a fraction with the change in y value on top, and the change of x value on the bottom. If we have two points (4, 1) and (0, -5) we can put this into a fraction - $\frac{-5-1}{0-4}$ , which simplifies down to -6/-4, or 3/2. Thus the answer is f(x)= $\frac{3}{2}$ x-5<span />