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klasskru [66]
3 years ago
6

Exercise 2.11 19) A function has f'(1)=3 and f(1)=5. Evaluate f(-2) given f''(x)=6x+18

Mathematics
1 answer:
ladessa [460]3 years ago
5 0
\int 6x+18\, dx=3x^2+18x+C\\\\
3=3\cdot 1^2+18\cdot1+C\\
3=3+18+C\\
C=-18\\
f'(x)=3x^2+18x-18\\\\
\int 3x^2+18x-18\, dx=x^3+9x^2-18x+C\\\\
5=1^3+9\cdot1^2-18\cdot1+C\\
5=1+9-18+C\\
C=13\\\\
f(x)=x^3+9x^2-18x+13


f(-2)=(-2)^3+9\cdot(-2)^2-18\cdot(-2)+13\\
f(-2)=-8+36+36+13\\
\boxed{f(-2)=77}

But honestly I don't know if it's good method.
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lions [1.4K]

Answer:

  4L +4W +16 square inches

Step-by-step explanation:

The area of the border is the equivalent of that of a rectangle with a width equal to the width of the border, and a length equal to the length of the midline of the border. That length is the perimeter of the rectangle that is L+2 units long and W+2 units wide.

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Then the border area is ...

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4 0
3 years ago
How many feet are in two mlies
mafiozo [28]
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4 years ago
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mafiozo [28]
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