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Consider the functions and , where . Find . The graphs of and have a common tangent at . Show that…
Consider the functions $f(x) = -(x-h)^2 + 2k$ and $g(x) = e^{x-2} + k$, where $h, k \in \mathbb{R}$.
(a)
Find $f'(x)$.
(b)
The graphs of $f$ and $g$ have a common tangent at $x = 3$. Show that: $2h = e + 6$.
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From ISC 2025 Practice Mathematics, question 91.