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SerGnik
@SerGnik
July 2022
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Составьте уравнения касательной:
1)y=x³-2x²+3x+4; x=2
2)y=x/4^4+x/2^2+2x-1; x=2
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Answers & Comments
SidaSlavi
1.
f(x) = x³-2x²+3x+4; x0=2
f(2) = 2^3 - 2*2^2 + 3*2 +4 = 8-8+6+4 = 10
f'(x0) = (x³-2x²+3x+4)'=3x^2 - 4x + 3
f'(2) = 3*2^2 - 4*2 +3 = 12 - 8 +3 = 7
Уравнение касательной:
y = f(x0) + f'(x0)(x - x0)
y = 10 +7*(x-2)
2.
f(x) = x/4^4+x/2^2+2x-1; x0=2
f(2) = (2/4)^4 + (2/2)^2 +2*2 -1 = 1/16 + 1 +4 -1 = 1/16 +4 = 65/16
f'(x) = (x/4^4+x/2^2+2x-1)' = x^3 + x + 2
f'(2) = 2^3 + 2 +2 = 8+2+2 = 12
Уравнение касательной:
y = 65/16 +12*(x-2)
2 votes
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Answers & Comments
f(x) = x³-2x²+3x+4; x0=2
f(2) = 2^3 - 2*2^2 + 3*2 +4 = 8-8+6+4 = 10
f'(x0) = (x³-2x²+3x+4)'=3x^2 - 4x + 3
f'(2) = 3*2^2 - 4*2 +3 = 12 - 8 +3 = 7
Уравнение касательной:
y = f(x0) + f'(x0)(x - x0)
y = 10 +7*(x-2)
2.
f(x) = x/4^4+x/2^2+2x-1; x0=2
f(2) = (2/4)^4 + (2/2)^2 +2*2 -1 = 1/16 + 1 +4 -1 = 1/16 +4 = 65/16
f'(x) = (x/4^4+x/2^2+2x-1)' = x^3 + x + 2
f'(2) = 2^3 + 2 +2 = 8+2+2 = 12
Уравнение касательной:
y = 65/16 +12*(x-2)