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Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityDifferentiabilityMedium2 minQB

MathematicsMediuminteger

If $f (x) = x^{3} + x^{2} f^{'} (1) + x f^{''} (2) + f^{'''} (4)$ , find $f (1)$ .

Answer:

Solution:

Differentiation and substitution at 1 and 2 give $f^{'} (1) = - 5$ and $f^{''} (2) = 2$ ; also $f^{'''} (4) = 6$ . Hence $f (x) =$ $x^{3} - 5 x^{2} + 2 x + 6$ , so $f (1) = 4$ .

Stream:JEESubject:MathematicsTopic:Continuity - DifferentiabilitySubtopic:Differentiability

⏱ 2mℹ️ Source: QB

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