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3 years ago

Find f(7) when f(x)=−5x+2.

Mathematics

1 answer:

VARVARA [1.3K]3 years ago

6 0

Answer:

-33

Step-by-step explanation:

Plug it in;

f(7)= -5(7)+2

-5(7)= -35+2= -33

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3 years ago

Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

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3 years ago

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3 years ago

If x=-5 what is the value of x^2-1/x+1? A. 6 b. -4 c. 4 d. 5 4/5 e. 19 need answers asap

xxTIMURxx [149]

Answer:

The answer is -6 but its not in the option

Step-by-step explanation:

$\frac{ {x}^{2} - 1 }{ x + 1}$

Let x = -5

[(-5)²-1]/(-5+1)

= (25-1)/(-4)

= 24/-4

= -6

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3 years ago