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SVETLANKA909090 [29]
3 years ago
7

Over which interval is the graph of f(x) = –x2 + 3x + 8 increasing?

Mathematics
2 answers:
vivado [14]3 years ago
7 0
Hello there!

To find the increasing intervals for this graph just based on the equation, we should find the turning points first.

Take the derivative of f(x)...
f(x)=-x²+3x+8
f'(x)=-2x+3

Set f'(x) equal to 0...
0=-2x+3
-3=-2x
3/2=x

This means that the x-value of our turning point is 3/2. Now we need to analyze the equation to figure out the end behavior of this graph as x approaches infinity and negative infinity.
Since the leading coefficient is -1, as x approaches ∞, f(x) approaches -∞ Because the exponent of the leading term is even, the end behavior of f(x) as x approaches -∞ is also -∞.

This means that the interval by which this parabola is increasing is...
(-∞,3/2)

PLEASE DON'T include 3/2 on the increasing interval because it's a turning point. The slope of the tangent line to the turning point is 0 so the graph isn't increasing OR decreasing at this point.

I really hope this helps!
Best wishes :)
Mashcka [7]3 years ago
6 0

Answer:

C

Step-by-step explanation:

the answer is C

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What is the average rate of change for the function f(x)=3x^2 -5 on the interval −3 ≤ x ≤ −1 ?
Anestetic [448]

Answer:

-12

Step-by-step explanation:

Let b = -1 and a = -3

The average rate of change = \frac{f(b) - f(a)}{b - a}

f(b) = f(-1) = 3(-1)^2 - 5 = 3 - 5 = -2

f(a) = f(-3) = 3(-3)^2 - 5 =27 - 5 = 22

f(b) - f(a) = -2 - 22 = -24

b - a = -1 + 3 = 2

\frac{f(b) - f(a)}{b - a} = -24/2 = -12

4 0
2 years ago
Can someone tell me what the lcd is??​
Ugo [173]
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7 0
2 years ago
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aniked [119]

Answer:

Where is the question?

Step-by-step explanation:

8 0
3 years ago
Find all of the zeros of each function <br>x^3+9x^2+6x-16​
dedylja [7]

Answer:

x = -8, -2, and 1

Step-by-step explanation:

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6 0
3 years ago
Roger is measuring the length of a hanging spring as various weights are added to it. Using these measurements, he obtained the
blondinia [14]
B.) the length of the spring increases by 0.006 cm for every gram added to it.
 y = 0.006x + 11.50
where:y = length of the spring in centimetersx = mass added to the spring in grams11.50 = the first number in the sequence0.006 = the common difference among numbers in the sequence.
x       y1      11.5 + 0.006(1) = 11.50 + 0.006 = 11.506  2      11.5 + 0.006(2) = 11.50 + 0.012 = 11.5123      11.5 + 0.006(3) = 11.50 + 0.018 = 11.5184      11.5 + 0.006(4) = 11.50 + 0.024 = 11.5245      11.5 + 0.006(5) = 11.50 + 0.030 = 11.530
For every 1 gram added, the length of the string increases by 0.006cm
hope this helps
3 0
2 years ago
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