Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingHard2 minQB

MathematicsHardsingle choice

Let $f$ be a cubic polynomial with a local maximum at $x = 2$ . Also, $f$ has a local minimum at $x = 4$ , and $f (2) = 12$ , $f (4) = 4$ . Define $G (t) = \int_{4 - t}^{4 + t} f (x) d x$ . Which describes $G$ on $R$ ?

Options:

Answer:

Solution:

The conditions give $f (x) = x^{3} /2 - 6 x^{2} + 18 x - 4$ , for which $f (4 - t) + f (4 + t) = 8$ . By Leibniz differentiation, $G^{'} (t) = f (4 + t) + f (4 - t) = 8 > 0$ , so $G$ is increasing.

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Increasing-Decreasing

⏱ 2mℹ️ Source: QB

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