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VladimirAG [237]
3 years ago
12

F(x)=(x-6)e^-3x find the interval in which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema

Mathematics
1 answer:
Over [174]3 years ago
5 0
\bf f(x)=(x-6)e^{-3x}\\\\
-----------------------------\\\\
\cfrac{dy}{dx}=1\cdot e^{-3x}+(x-6)-3e^{-3x}\implies \cfrac{dy}{dx}=e^{-3x}[1-3(x-6)]
\\\\\\
\cfrac{dy}{dx}=e^{-3x}(19-3x)\implies \cfrac{dy}{dx}=\cfrac{19-3x}{e^{3x}}

set the derivative to 0, solve for "x" to get any critical points
keep in mind, setting the denominator to 0, also gives us critical points, however, in this case, the denominator will never be 0, so... no critical points from there

there's only 1 critical point anyway, and do a first-derivative test on it, check a number before it and after it, to see what sign the derivative has, and thus, whether the graph is going up or down, to check for any extrema
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3. 'a' and 'b' are the intercepts made
Julli [10]

Given:

'a' and 'b' are the intercepts made  by a straight-line with the co- ordinate axes.

3a = b and the line  pass through the point (1, 3).

To find:

The equation of the line.

Solution:

The intercept form of a line is

\dfrac{x}{a}+\dfrac{y}{b}=1         ...(i)

where, a is x-intercept and b is y-intercept.

We have, 3a=b.

\dfrac{x}{a}+\dfrac{y}{3a}=1           ...(ii)

The line  pass through the point (1, 3). So, putting x=1 and y=3, we get

\dfrac{1}{a}+\dfrac{3}{3a}=1

\dfrac{1}{a}+\dfrac{1}{a}=1

\dfrac{2}{a}=1

Multiply both sides by a.

2=a

The value of a is 2. So, x-intercept is 2.

Putting a=2 in b=3a, we get

b=3(2)

b=6

The value of b is 6. So, y-intercept is 6.

Putting a=2 and b=6 in (i), we get

\dfrac{x}{2}+\dfrac{y}{6}=1

Therefore, the equation of the required line in intercept form is \dfrac{x}{2}+\dfrac{y}{6}=1.

5 0
2 years ago
O
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Answer:

4.) ET is perpendicular to plane BAT

Step-by-step explanation:

4 0
3 years ago
Please help. Only if you know it.
andrew11 [14]

Answer:

C (Lake Depth Answer)

Step-by-step explanation:

Here we want to find the math that <u>ends up with 0</u>.

The stock starts with 12$, but loses 16$.

That's -4$ total, not 0.

The ion starts with 19 protons, and 18 electrons. Protons are postive charges, electrons are negative.

This leaves us with 1 proton, not 0.

The lake depth increases by 6 inches, but evaporates 6.

This leaves us back where we started, with 0.

Ahmed spends 25$, but earns 30$.

This leaves us with $5, not 0.

5 0
3 years ago
Rút gọn (x-4) (x-3) -x(x+5) +82
WINSTONCH [101]

Answer:

-12x + 94

Step-by-step explanation:

Simplify:

\left(x-4\right)\left(x-3\right)-x\left(x+5\right)+82

=x^2-7x+12-x\left(x+5\right)+82

=x^2-7x+12-x^2-5x+82

=x^2-x^2-7x-5x+12+82

=-7x-5x+12+82

=-7x-5x+94

=-12x+94

5 0
2 years ago
Can somewon help me plz can somewon help me
Karolina [17]

Hey there! I'm happy to help!

Let's look at our diameters.

1*10^2^1\\5*10^2^2

We want to see how many times greater the diameter of the IC 1101 is than the Milky Way. So, we will divide it's diameter by the diameter of the Milky Way.

\frac{5*10^2^2}{1*10^2^1} \\

We divide the numbers without exponents, giving us 5. Then, we divide the 10s with exponents. When dividing exponents, you subtract the numbers in the exponent to get your result. For example, x³÷x²=x

\frac{5*10^2^2}{1*10^2^1} = 5*10=50

Therefore, your answer is 50.

Have a wonderful day! :D

3 0
3 years ago
Read 2 more answers
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