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maks197457 [2]
3 years ago
9

Use both the first and second derivative tests to show that f(x) = 3x2 − 6x + 1 has a relative minimum at x=1.

Mathematics
1 answer:
Vlada [557]3 years ago
8 0

Step-by-step explanation:

Given: f(x) = 3x^2 − 6x + 1.      x ∈ (-∞, ∞)

now differentiating f(x) w.r.t. x we get

f'(x) = 6x-6

equating it 0 we get

x = 1, which is a critical point

Now using second derivative test to check relative maxima or minima

f''(x) = 6 >0

⇒ x=1 is a relative minima.

also, x=1 f(1) = 3-6+1 = -2

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In a class of 120 students, 65% have at least
Zigmanuir [339]

We need to find how many students have at least one social media account.

We know that there are 120 students in the class.

We also know that there are 65% of students that have at least one social media account.

To find your answer, would multiply 120 by 0.65:

120 · 0.65 = 78

This means that 78 of the students has at least one social media account.

Answer:

78 students

4 0
3 years ago
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
m_a_m_a [10]

Answer:

Line of "rise": (0, 3) to (0, 0) ==> -3 units

Line of "run": (0, 0) to (1, 0) ==> 1 unit

Slope: rise/run ==> -3/1

Step-by-step explanation:

Slope is basically a ratio of changes in the y-value to changes in the x-value. What I mean by that is the slope shows how much the line goes up or down compared to how much the line goes left or right. In this case, the line goes right one unit for every 3 units the line goes down. Taking a look at the portion of the line in Quadrant 1 (top right quadrant), the line starts at (0, 3) and ends at (1, 0). I guess that's another way to figure out slope, too: line up the two coordinates (the leftmost one above the rightmost one), and add or subtract.

Like this:

    (0, 3)

<u>     (1,  0)     </u>

   +1   -3

Since the formula for slope is rise/run (y-difference/x-difference), the slope is therefore -3/+1, or simply -3/1. (You don't include plus signs.)

3 0
3 years ago
Please help if you can. I will give Brainiest to best answer. This question is a Calculus/Trigonometry question. I ask that you
Ierofanga [76]

7 is incorrect. The answer should be -4. Here's how I'd derive it:

\tan^2\dfrac x2=\dfrac{\sin^2\frac x2}{\cos^2\frac x2}=\dfrac{\frac{1-\cos x}2}{\frac{1+\cos x}2}=\dfrac{1-\cos x}{1+\cos x}

With \pi, we should expect \cos x. If \tan x=\dfrac8{15}, then

\sec x=-\sqrt{1+\tan^2x}=-\dfrac{17}{15}\implies\cos x=-\dfrac{15}{17}

Also,

\pi

so we should expect \tan\dfrac x2 and

\tan\dfrac x2=-\sqrt{\dfrac{1-\cos x}{1+\cos x}}=-4

You seem to be taking

\tan\dfrac x2=\dfrac{1+\cos x}{-\sin x}

but this is not an identity.

###

8 is incorrect. Just a silly mistake, you swapped the order of the terms in the numerator. It should be

\dfrac{\sqrt6-\sqrt2}4

###

9. Use the identity from (7). \dfrac{7\pi}{12} lies in the second quadrant, so

\tan\dfrac{7\pi}{12}=-\sqrt{\dfrac{1-\cos\frac{7\pi}6}{1+\cos\frac{7\pi}6}}=-\sqrt{7+4\sqrt3}=-2-\sqrt3

###

12.

\dfrac{\cot x-1}{1-\tan x}=\dfrac{\frac{\cos x}{\sin x}-1}{1-\frac{\sin x}{\cos x}}

=\dfrac{\cos x(\cos x-\sin x)}{\sin x(\cos x-\sin x)}

=\dfrac{\cos x}{\sin x}

=\dfrac{\csc x}{\sec x}

###

13.

\dfrac{1+\tan x}{\sin x+\cos x}=\dfrac{1+\frac{\sin x}{\cos x}}{\sin x+\cos x}

=\dfrac{\cos x+\sin x}{\cos x(\sin x+\cos x)}

=\dfrac1{\cos x}

=\sec x

###

14.

\sin2x(\cot x+\tan x)=2\sin x\cos x\left(\dfrac{\cos x}{\sin x}+\dfrac{\sin x}{\cos x}\right)

=2\sin x\cos x\dfrac{\cos^2x+\sin^2x}{\sin x\cos x}

=2

###

15.

\dfrac{1-\tan^2\theta}{1+\tan^2\theta}=\dfrac{1-\frac{\sin^2\theta}{\cos^2\theta}}{1+\frac{\sin^2\theta}{\cos^2\theta}}

=\dfrac{\cos^2\theta-\sin^2\theta}{\cos^2\theta+\sin^2\theta}

=\cos2\theta

3 0
3 years ago
danielle wants to buy a car on loan. in order to pay the least possible amount in interest over the loan term, what should she d
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If Danielle wants to buy a car on a loan and she wanted the least possible amount of payment in paying its interest over the loan term, to answer it.. Danielle should pay up a higher amount of principal and she should check the interest rate offered by the loaner. There are different bracketing of interest in loan terms.
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4 years ago
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Solve the formula h=54t+12at2 h = 54 t + 1 2 a t 2 for a.
oee [108]
Hope this helps!!!!!

3 0
3 years ago
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