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AlexFil1
@AlexFil1
July 2022
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Удачник66
Verified answer
F(x) = 3x^2 - 4√x + 8; x0 = 1; f(x0) = f(1) = 3*1 - 4*√1 + 8 = 7
f'(x) = 6x - 4/(2√x) = 6x - 2/√x; f'(x0) = f'(1) = 6 - 2/1 = 4
Уравнение касательной к кривой:
y(x) = f(x0) + f'(x0)*(x - x0)
y(x) = 7 + 4(x - 1) = 7 + 4x - 4 = 4x + 3
Точки пересечения с осями
y(0) = 3; A(0; 3)
4x + 3 = 0; x = -3/4; B(-3/4; 0)
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Answers & Comments
Verified answer
F(x) = 3x^2 - 4√x + 8; x0 = 1; f(x0) = f(1) = 3*1 - 4*√1 + 8 = 7f'(x) = 6x - 4/(2√x) = 6x - 2/√x; f'(x0) = f'(1) = 6 - 2/1 = 4
Уравнение касательной к кривой:
y(x) = f(x0) + f'(x0)*(x - x0)
y(x) = 7 + 4(x - 1) = 7 + 4x - 4 = 4x + 3
Точки пересечения с осями
y(0) = 3; A(0; 3)
4x + 3 = 0; x = -3/4; B(-3/4; 0)