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Olenka [21]
3 years ago
14

Ex 2.8 3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1

Mathematics
1 answer:
harkovskaia [24]3 years ago
4 0
y=x^5-3\\ y'=5x^4\\\\ 5x^4=0\\ x=0\\ 0\in [-2,1]\\\\ y''=20x^3\\\\
y''(0)=20\cdot0^3=0

The value of the second derivative for x=0 is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
But the value of 5x^4 is always positive for x\in\mathbb{R}\setminus \{0\}. That means at x=0 there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval [-2,1].
The function y is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.

y_{max}=y(1)=1^5-3=-2
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RideAnS [48]

Answer:

y=\underline {1.5}x+\underline 0

Step-by-step explanation:

From the graph,

The initial red incline is a straight line passing through the origin.

So, a straight line passing through the origin is of the form:

y=mx+0

Where, 'm' is the slope.

Now, the slope of a given as the change in y value to change in x value.

Consider the two end points of the red line (0, 0) and (4, 6).

The slope with two points (x_1,y_1)\ and\ (x_2,y_2) on the line is given as:

m=\frac{(y_2-y_1)}{(x_2-x_1)}

Plug in x_1=0,y_1=0,x_2=4,y_2=6. Therefore, slope is:

m=\frac{6-0}{4-0}\\m=\frac{6}{4}=1.5

Hence, the equation of the initial red incline is:

y=\underline {1.5}x+\underline 0

3 0
3 years ago
Roger's Cafe has usual daily earnings of $800. Today, the cafe earned 120% of the usual daily earnings. How much did they earn t
riadik2000 [5.3K]

Answer:

960

Step-by-step explanation:

Over here, I'm going to do it in two ways, and either way works, one is just easier to do out:

1st way:

You can represent the percent 120 as a decimal which is 1.20, then you do 800*1.2.

2nd way:

You can use benchmark percents. You find 10 percent of 800 which is 80 and multiply 80 by 2 to get 160, so 20% is 160 dollars. Then you add 160 to 800 (800+160) and get 960.

Please tell me if you have any questions.

8 0
3 years ago
Find the equation of a line that goes through points (-3, -5) and (-1, -2).
ivann1987 [24]

The slope-point formula:

y-y_1=m(x-x_1)

The formula of a slope: m=\dfrac{y_2-y_1}{x_2-x_1}

We have:

(-3,-5)\to x_1=-3,\ y_1=-5\\(-1,-2)\to x_2=-1,\ y_2=-2

Substitute and calculate:

m=\dfrac{-2-(-5)}{-1-(-3)}=\dfrac{3}{2}=1.5\\\\y-(-5)=1.5(x-(-3))\\\\y+5=1.5(x+3)\\\\y+5=1.5x+4.5\ \ \ |-5\\\\y=1.5x-0.5

7 0
3 years ago
Can you please help me this is coordinates only and thank you.
nataly862011 [7]

Answer: (2,6)

Step-by-step explanation: you go the the left 3 from F then up 2 and you have it.

3 0
3 years ago
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