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Let , where . Show that . The graph of has exactly one maximum point at P. Find the -coordinate of…
Let $f(x) = \frac{\log 5x}{kx}$, where $x > 0, k \in \mathbb{R}^+$.
(a)
Show that $f'(x) = \frac{1-\log 5x}{kx^2}$.
(b)
The graph of $f$ has exactly one maximum point at P. Find the $x$-coordinate of P.
(c)
Find $f''(x)$.
(d)
Find the value of $x$ for which $f''(x)$ vanishes.
Answer
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From ISC 2025 Practice Mathematics, question 93.