Mathematics: Find y=f(x) if f (x)=6x-2, f (1)=3, and f(2)=7

Find y=f(x) if f (x)=6x-2, f (1)=3, and f(2)=7 - id62132715309022, Tcareyoliver

Ответ:

odriskel49

18.02.2022

Mathematics

f(x)=x^3-x^2+2x-1

Step-by-step explanation:

Since f''(x)=6x-2 , then f'(x)=3x^2-2x+C , thus:

$f'(x)=3x^2-2x+C\\\\f'(1)=3(1)^2-2(1)+C\\\\3=3-2+C\\\\3=1+C\\\\2=C$

Therefore, since f'(x)=3x^2-2x+2 , then f(x)=x^3-x^2+2x+C , thus:

$f(x)=x^3-x^2+2x+C\\\\f(2)=2^3-2^2+2(2)+C\\\\7=8-4+4+C\\\\7=8+C\\\\-1=C$

In conclusion, f(x)=x^3-x^2+2x-1

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Ответ:

punani

14.02.2022

Mathematics

x=10.5

Step-by-step explanation:

Use Thales' Theorem which says: If two lines, not necessarily parallel, are cut by a system of parallel lines, then the segments that result on one of the two lines are proportional to the corresponding segments obtained on the other.

Take a look at the picture I attached you, from it, It is true that:

$\frac{AB}{A'B'} =\frac{BC}{B'C'}$

Hence:

$\frac{12}{6} =\frac{21}{x}$

Solving for x:

$x=\frac{21}{2} =10.5$

Using the following diagram, solve for x.

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Find y=f(x) if f''(x)=6x-2, f'(1)=3, and f(2)=7

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