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NNADVOKAT [17]
3 years ago
12

What expressions makes y to the third power

Mathematics
1 answer:
siniylev [52]3 years ago
6 0

Answer:

y^3

Step-by-step explanation:

the exponent 3 raises a number to the third power

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Find the absolute extrema of f(x) = e^{x^2+2x}f ( x ) = e x 2 + 2 x on the interval [-2,2][ − 2 , 2 ] first and then use the com
fredd [130]

f(x)=e^{x^2+2x}\implies f'(x)=2(x+1)e^{x^2+2x}

f has critical points where the derivative is 0:

2(x+1)e^{x^2+2x}=0\implies x+1=0\implies x=-1

The second derivative is

f''(x)=2e^{x^2+2x}+4(x+1)^2e^{x^2+2x}=2(2x^2+4x+3)e^{x^2+2x}

and f''(-1)=\frac2e>0, which indicates a local minimum at x=-1 with a value of f(-1)=\frac1e.

At the endpoints of [-2, 2], we have f(-2)=1 and f(2)=e^8, so that f has an absolute minimum of \frac1e and an absolute maximum of e^8 on [-2, 2].

So we have

\dfrac1e\le f(x)\le e^8

\implies\displaystyle\int_{-2}^2\frac{\mathrm dx}e\le\int_{-2}^2f(x)\,\mathrm dx\le\int_{-2}^2e^8\,\mathrm dx

\implies\boxed{\displaystyle\frac4e\le\int_{-2}^2f(x)\,\mathrm dx\le4e^8}

5 0
3 years ago
Which equation is the inverse of y = 100 - x??
denis-greek [22]

For this case we must find the inverse of the following function:

y = 100-x

To do this, we follow the steps below:

We exchange the variables:

x = 100-y

We clear the variable "x" (the variable is already cleared):

x = 100-y

We change "x" to "y":

y = 100-x

We change y for f^{-1}(x):

f^{-1} (x) = 100-x

ANswer:

f^{-1} (x) = 100-x

4 0
3 years ago
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