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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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If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
Dovator [93]

Keywords

quadratic equation, discriminant, complex roots, real roots

we know that

The formula to calculate the <u>roots</u> of the <u>quadratic equation</u> of the form  ax^{2} +bx+c=0 is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}

where

The <u>discriminant</u> of the <u>quadratic equation</u>  is equal to

b^{2}-4ac

if  (b^{2}-4ac)> 0 ----> the <u>quadratic equation</u> has two <u>real roots</u>

if  (b^{2}-4ac)=0 ----> the <u>quadratic equation</u> has one <u>real root</u>

if  (b^{2}-4ac)< 0 ----> the <u>quadratic equation</u> has two <u>complex roots</u>

in this problem we have that

the <u>discriminant</u> is equal to -8

so

the <u>quadratic equation</u> has two <u>complex roots</u>

therefore

the answer is the option A

There are two complex roots

5 0
3 years ago
Read 2 more answers
Estimate a 15% tip for a 26.80 meal
lina2011 [118]
26.80 x .15 gives you the answer, which is $4.02 in tip
7 0
3 years ago
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A piece of property lies between two parallel streets as shown. m&lt;1=(2x+6)°,and m&lt;2=(3x+9)°. What is the relationship betw
kolezko [41]
  • The angles are supplementary angles
  • The measure of angle m<1 and m<2 are 72 and 108 degrees respectively

Find the diagram attached. From the figure, the sum of the angles m<1 and m<2 are supplementary

Given the following angles

m<1 = 2x + 6

m<2 = 3x + 9

Since both angles are supplementary, hence;

2x + 6 + 3x + 9 = 180

5x + 15 = 180

5x = 180 - 15

5x = 165

x = 165/5

x = 33

Get the measure of m<1;

m<1 = 2x + 6

m<1 = 2(33) + 6

m<1 = 66 + 6

m<1 = 72degrees

Get the measure of m<2:

m<2 = 180 - m<1

m<2 = 180 - 72

m<2 = 108degrees

Hence the measure of angle m<1 and m<2 are 72 and 108 degrees respectively

Learn more here: brainly.com/question/22309882

5 0
2 years ago
Need help, please.............................
Bogdan [553]

Answer:

i DON'T KNOW THE ANSWER

Step-by-step explanation:

I DONT KNOW THE ANSWER ALL I KNOW IS TO USE BATMAN IF YOU KNOW WHAT THAT IS AND YEAH YOU WILL FIND THE ANSWER

4 0
3 years ago
Help me iv been trying from this morning
GalinKa [24]

Answer:

i did the first

Step-by-step explanation:

1st way

Standard form: a(X-h)²+k = ( -2/3X² -16/3X -32/3) +32/3 -17/3 = -2/3(X +4)² +5

y = -2/3*X^2-16/3*X-17/3

X = -4 ±√( 15/2) = -6.7386, or -1.2614

Axis of symmetry: X= -4; Vertex (maximum)=(h,k)=( -4, 5); y-intercept is (0,-5.66666666667)

two real roots: X=-1.2613872124776866 and -6.738612787477313

5 0
2 years ago
Read 2 more answers
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