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Question
Suppose f(x) `{:(= "p"x + 3",", "for" "a" ≤ x ≤ "b"),(= 5x^2 − "q"",", "for" "b" < x ≤ "c"):}`
Find the condition on p, q, so that f(x) is continuous on [a, c], by filling in the blanks.
f(b) = ______
`lim_(x -> "b"^+) "f"(x)` = _______
∴ pb + 3 = _______ − q
∴ p = `"_____"/"b"` is the required condition
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Solution
f(b) = pb + 3
`lim_(x -> "b"^+) "f"(x)` = 5b2 − q
∴ pb + 3 = 5b2 − q
∴ p = `(5"b"^2 - "q" - 3)/"b"` is the required condition.
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