Let $f(x)$ be a polynomial function such that $f(x) + f'(x) + f''(x) = {x^5} + 64.$ Then, the value of $\mathop {\lim }\limits_{x \to 1} \frac{{f(x)}}{{x - 1}}$ is equal to

JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

Let

f(x)

be a polynomial function such that

f(x) + f'(x) + f''(x) = {x^5} + 64.

Then, the value of

\lim\limits_{x \to 1} \frac{{f(x)}}{{x - 1}}

is equal to

View answer and explanation

Correct option: A

– 15

Option B (– 60) is correct because by substituting a general 5th-degree polynomial and using L'Hopital's rule, the limit can be found to be -15.

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