Assertion : $f (x) = \int_{1}^{x} {2 (t - 1) {(t - 2)}^{3} + 3 {(t - 1)}^{2} {(t - 2)}^{3}} d t$ attains a maximum at $x = 2$ Reason: The value of $f^{'} (x) = 0$ at $x = 1, 2$ and $\frac{7}{5}$ .

Both Assertion & Reason are individually correct and the Reason is not the correct explanation of Assertion

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Both Assertion & Reason are individually correct but Reason is not the correct (proper) explanation of Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is D Assertion is incorrect but Reason is correct
$f^{'} (x) = 2 (x - 1) {(x - 2)}^{3} + 3 (x - 1) {(x - 2)}^{2} = (x - 1) {(x - 2)}^{2} [5 x - 7)$
Hence Assertion is false and reason is true

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Assertion :f(x)=∫x1{2(t−1)(t−2)3+3(t−1)2(t−2)3}dt attains a maximum at x=2 Reason: The value of f′(x)=0 at x=1,2 and 75.

The correct option is D Assertion is incorrect but Reason is correctf′(x)=2(x−1)(x−2)3+3(x−1)(x−2)2=(x−1)(x−2)2[5x−7)Hence Assertion is false and reason is true

Assertion : $f (x) = \int_{1}^{x} {2 (t - 1) {(t - 2)}^{3} + 3 {(t - 1)}^{2} {(t - 2)}^{3}} d t$ attains a maximum at $x = 2$ Reason: The value of $f^{'} (x) = 0$ at $x = 1, 2$ and $\frac{7}{5}$ .

The correct option is D Assertion is incorrect but Reason is correct
$f^{'} (x) = 2 (x - 1) {(x - 2)}^{3} + 3 (x - 1) {(x - 2)}^{2} = (x - 1) {(x - 2)}^{2} [5 x - 7)$
Hence Assertion is false and reason is true