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zzz [600]
2 years ago
5

Given f(x)=-2x^3 + 3x^2 , find the equation of that tangent line of f at the point where x=2.

Mathematics
1 answer:
trapecia [35]2 years ago
5 0

Step 1: Find f'(x):

f'(x) = -6x^2 + 6x

Step 2: Evaluate f'(2) to find the slope of the tangent line at x=2:

f'(2) = -6(2)^2 + 6(2) = -24 + 12 = -12

Step 3: Find f(2), so you have a point on y=f(x):

f(2) = -2·(2)^3 + 3·(2)^2 = -16 + 12 = -4

So, you have the point (2,-4) and the slope of -12.

Step 4: Find the equation of your tangent line:

Using point-slope form you'd have: y + 4 = -12 (x - 2)

That is the equation of the tangent line.

If your teacher is picky and wants slope-intercept, solve that for y to get:

y = -12 x + 20

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3. start fraction x over 5 end fraction + 6 = 10 (1 point) 44 30 20 –20 4. 3(4 – 2x) = –2x (1 point) –1 1 2 3
max2010maxim [7]

Answer:

3.x=20


Step-by-step explanation:


5 0
3 years ago
Wheel I has diameter 23.4. Wheel ll has diameter 18.0. Round the diameter of each wheel to the nearest inch. About how much fart
11111nata11111 [884]

Answer:

Wheel1 = 147inches , wheel 2 = 113inches

Wheel 1 will travel 147 revolutions.

Step-by-step explanation:

Finding the circumference of both wheels

Wheel 1 = 2 pi r = 2 × 3.142 × 23.4 = 147.05 inches. To the nearest inches = 147inches

Wheel 2 = 2 pi × r = 2 × 3.142 × 18 = 113.11inches . To the nearest inches = 113inches.

I rotation = 1 revolution

In 1 rotation, wheel 1 will travel= 147 × 1 = 147 revolutions.

8 0
3 years ago
Read 2 more answers
Steven earns extra money babysitting. He charges $26.25 for 3 hours and $70.00 for 8 hours.
AlekseyPX
The answer is Y = 8.75x
4 0
3 years ago
Read 2 more answers
Y=-2x graphed. had to put more words to put this out
timurjin [86]

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0, or (0,y))


slope=\frac{rise}{run}

Rise is the number of units you go up(+) or down(-)

Run is the number of units you go to the right


y = -2x

This has a y-intercept of 0, so the line intersects the y-axis/goes through the origin at (0,0)

The slope is -2 or \frac{-2}{1}, so from each point, you go down 2 units, and to the right 1 unit.

5 0
3 years ago
Describe the center and spread of the data using either the mean and standard deviation or the five-number summary. Justify your
goblinko [34]

Answer:

The distribution is skewed, so use the five-number summary. range: 38, median: 16, half of the data are between 9.5 and 25

Step-by-step explanation:

In the picture attached the histogram is shown. We can see that data is skewed to the right, so we have to use the five-number summary. The range of the data is 39 - 1 = 38 (subtraction of the maximum value to the minimum value); the median is (15 + 17)/2 = 16 (if you order the values, 15 and 17 are in the middle); quartile 1 is 9.25 and quartile 3 is 25.5 (see diagram of box and whisker attached), then half of the data are between those values.

8 0
3 years ago
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