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Leno4ka [110]
1 year ago
13

Given f"(x) = 2, f'(1)=4, and f(2)=-2, find f(x).

Mathematics
1 answer:
Anna [14]1 year ago
6 0

Answer:

Step-by-step explanation:

f"(x)=2

integrating

f'(x)=2x+c

f'(1)=2+c=4

c=4-2=2

f'(x)=2x+2

integrating

f(x)=2x^2/2+2x+a

f(x)=x^2+2x+a

f(2)=-2

(2)^2+2(2)+a=-2

4+4+a=-2

a=-2-8=-10

f(x)=x^2+2x-10

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Step-by-step explanation:

☄ \underline{ \underline{ \text{Question }}}: The ratio of new houses to antique houses in a village is 4 : 5 . If there are 12 new houses , how many antique houses are there ?

☄\underline{ \underline{ \text{Solution}}} :

✏ Let , the number of antique houses in a village be ' x ' .

Then , According to the question :

\sf{ \frac{Number \: of \: new \: houses}{Number \: of \: antique \: houses}  \:  =  \:  \frac{4}{5}}

⤑\sf{ \frac{12}{x}  =  \frac{4}{5}}

Apply cross product property

⤑\sf{4 \times x = 12 \times 5}

⤑\sf{4x = 60}

⤑\sf{ \frac{4x}{4}  =  \frac{60}{4}}

⤑\sf{x = 15}

So, The number of antique houses in a village is 15.

\red{ \boxed{ \boxed{ \tt{Our \: final \: answer :  \boxed{ \bold{15}}}}}}

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Answer:

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