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Home » Why These 5 Interview Looks Are Guaranteed to Turn Heads & Get You Hired! - Sterling Industries

Why These 5 Interview Looks Are Guaranteed to Turn Heads & Get You Hired! - Sterling Industries

📅 April 19, 2026 👤 scraface

Apr 19, 2026

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📌 Solve for \( x \) in the equation \( 3x + 4 = 2x + 10 \).

📌 Subtract \( 2x \) from both sides: \( x + 4 = 10 \).

📌 Subtract 4 from both sides: \( x = 6 \).

📌 Find the derivative of \( f(x) = 3x^2 + 5x - 7 \).

📌 Using the power rule, \( \frac{d}{dx}[x^2] = 2x \) and \( \frac{d}{dx}[x] = 1 \).

📌 Thus, \( f'(x) = 6x + 5 \).

📌 #### 6x + 5

📌 If a train travels at 60 km/h for 2.5 hours, how far does it travel?

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u^2 = \sin^2 x + 2\sin x \cos x + \cos^2 x = 1 + 2\sin x \cos x
\Rightarrow \sin x \cos x = \frac{u^2 - 1}{2}
f(x) = \left(\frac{u}{\frac{u^2 - 1}{2}}\right)^2 = \left(\frac{2u}{u^...
Now, since \(0 < x < \frac{\pi}{2}\), \(u = \sin x + \cos x = \sqrt{2}...
Let \(v = u^2\), so \(v \in (1, 2]\). Then:
f(x) = \frac{4v}{(v - 1)^2}
Let \(g(v) = \frac{4v}{(v - 1)^2}\). Find maximum on \(v \in (1, 2]\).
Take derivative:
g'(v) = \frac{4(v - 1)^2 - 4v \cdot 2(v - 1)}{(v - 1)^4} = \frac{4(v -...
For \(v > 1\), \(g'(v) < 0\), so \(g(v)\) is decreasing on \((1, 2]\)....

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