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Temka [501]
3 years ago
11

Find f(-2) for the function f (x) = 3x^2-2x+7

Mathematics
1 answer:
barxatty [35]3 years ago
4 0

Answer:

23

Step-by-step explanation:

plug -2 in for x then solve

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Factor completely.
Serga [27]
Factor the polynomial:

4u² – 20u + 25

Rewrite – 20u as – 10u – 10u, and then factor it by grouping:

= 4u² – 10u – 10u + 25

= 2u * (2u – 5) – 5 * (2u – 5)

= (2u – 5) * (2u – 5)

= (2u – 5)² <––– this is the answer.

I hope this helps. =)
5 0
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 <em>f</em> :

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 <em>g</em> :

\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 <em>n</em> 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 <em>f</em> has a minimum of -7 and a maximum of 299.

4 0
3 years ago
A florist received 30 dozen roses. She order 20 dozen. What percent did she receive in excess
KonstantinChe [14]
Extra 10, 10 is half of what she ordered so she received an extra 50%
8 0
2 years ago
Read 2 more answers
Cual es la ecuación de la recta vertical que pasa por (2,3)?
NeTakaya

Answer:

a

Step-by-step explanation:

6 0
3 years ago
Let f(x) be a continuous function such that f(1) and f'(x)-Vx3 + 6. What is the value of,f(5)? (A) 11.446 (C) 24.672 (B) 13.446
tia_tia [17]

Answer:

f(5) = 26.672 which is option D

Step-by-step explanation:

From question, f(1) = 2 and f'(x)=√(x^3 + 6)

f(5) = f(1) + (5,1)∫ f'(x) dx

Integrating using the boundary 5 and 1;

f(5) = 2 + (5,1)∫√(x^3 + 6) dx

f(5) = 2 + 24.672

So f(5) = 26.672

7 0
3 years ago
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