AP EAMCET · Maths · Application of Derivatives
If the function \(y=g(x)\) representing the slopes of the tangents drawn to the curve \(y=3 x^4-5 x^3-12 x^2+18 x+3\) is strictly increasing then the domain of \(g(x)\) is
- A \(\left[-\frac{1}{2}, \frac{4}{3}\right]\)
- B \(\left(\frac{-1}{2}, \frac{4}{3}\right)\)
- C \(\mathbb{R}-\left(\frac{-1}{2}, \frac{3}{4}\right)\)
- D \(\mathbb{R}-\left[\frac{-1}{2}, \frac{4}{3}\right]\)
Answer & Solution
Correct Answer
(D) \(\mathbb{R}-\left[\frac{-1}{2}, \frac{4}{3}\right]\)
Step-by-step Solution
Detailed explanation
\(g(x) = \frac{dy}{dx} = 12x^3 - 15x^2 - 24x + 18\) \(g'(x) = 36x^2 - 30x - 24\) \(g'(x) > 0 \implies 36x^2 - 30x - 24 > 0\) \(6x^2 - 5x - 4 > 0\) \((6x+3)(x-4/3) > 0 \implies 6(x+\frac{1}{2})(x-\frac{4}{3}) > 0\) \((x+\frac{1}{2})(x-\frac{4}{3}) > 0\) \(x \frac{4}{3}\) Domain:…
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