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3 years ago

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Determine whether Rolle's Theorem can be applied to f(x)=(x-1) (x-2)(x-3) on the closed interval [1,3]. Of Rolle's Theorem can b

e applied, find all values of c in the open interval (1,3) such that f'(c)=0

1 answer:

NeX [460]3 years ago

6 0

Answer:56

Step-by-step explanation:

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3 years ago

Enter the equation of the line in slope-intercept form. Slope is -1/2, and (-9,4) is on the line. The equation of the line is y=

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Answer:

$y=\displaystyle-\frac{1}{2}x-\displaystyle\frac{1}{2}$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where <em>m</em> is the slope and <em>b</em> is the y-intercept (the value of y when x is 0)

<u>1) Plug in the slope (</u><u><em>m</em></u><u>)</u>

We're given that the slope is $\displaystyle-\frac{1}{2}$ . In $y=mx+b$ , replace <em>m</em> with $\displaystyle-\frac{1}{2}$ :

$y=\displaystyle-\frac{1}{2}x+b$

<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>

$y=\displaystyle-\frac{1}{2}x+b$

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Subtract $\displaystyle\frac{9}{2}$ from both sides to isolate <em>b</em>:

$4-\displaystyle\frac{9}{2}=\displaystyle\frac{9}{2}+b- \displaystyle\frac{9}{2}\\\\\displaystyle-\frac{1}{2} = b$

Therefore, the y-intercept is $\displaystyle-\frac{1}{2}$ . Plug this back into $y=\displaystyle-\frac{1}{2}x+b$ as <em>b</em>:

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I hope this helps!

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