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Existence of Limit

Statement 1: ...

Question

Statement 1: The quadratic equation 10x²-28x+17=0 has atleast one root, belongs to[1,2].

Statement 2: f(x)=e^10x(x-1)(x-2) satisfy all the condition of Rolle's theorem in [1,2].

Which statement is true and which is the correct explanation of the second?

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Solution

The second statement is true.

Statement 1 can rewritten as : The quadratic equation 10x2-28x+17=0 has no root, belongs to[1,2].

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Similar questions

10 x^{2} - 28 x + 17 = 0

[1, 2]

f (x) = e^{10 x} (x - 1) (x - 2)

[1, 2]

f (x)

[1, 2]

f (x)

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\int_{1}^{2} f^{'} (x) d x

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\int_{1}^{2} f^{'} (x) d x

1 :

f (x) = (x - 1) | x - 1 |

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2 : | x - 1 |

x = 1

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2 \int 1 f^{'} (x) d x

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