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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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3 years ago
Please help! Find the equation of the line (graph provided in attached picture) Use exact numbers. y =_ x+_ ( _ represent blanks
Dennis_Churaev [7]

Answer:

y = \frac{3}{4}x - 2

Step-by-step explanation:

Equation of a line is given as y = mx + b

Where,

m = slope of the line = \frac{y_2 - y_1}{x_2 - x_1}

b = y-intercept, which is the value at the point where the line intercepts the y-axis. At this point, x = 0.

Let's find m and b to derive the equation for the line.

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

Use the coordinate pair of any two points on the line. Let's use the following,

(0, -2) = (x_1, y_1) => on the line, when x = 0, y = -2

(4, 1) = (x_2, y_2) => on the line, when x = 4, y = 1

Plug in the values and solve for m

m = \frac{1 - (-2)}{4 - 0}

m = \frac{1 + 2}{4}

m = \frac{3}{4}

b = -2 (the line intercepts the y-axis at this point)

Our equation would be =>

y = mx + b

y = \frac{3}{4}x + (-2)

y = \frac{3}{4}x - 2

5 0
3 years ago
Please answer quickly!!!!
Natalka [10]
The volume of the rectangular prism can be found with the formula
v= length × width × height
V = 10×10×30 = 3000

the volume of the triangular prism can be found with
v = 1/2(base×width×height)
v=1/2×30×9×10 = 1/2×2700
v = 1350

Now add the two volumes together for the total volume...

3000+1350 = 4,350 in^3
5 0
3 years ago
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