Question

If f(x) = px⁵ + qx⁴ + 5x³ - 10 has local maximum and minimum at x = 1 and x = 3 respectively then (p, q) = ______.

Options

• (0, 1)

• (1, -5)

• (1, 0)

• (3, -5)

Answer 1

If f(x) = px⁵ + qx⁴ + 5x³ - 10 has local maximum and minimum at x = 1 and x = 3 respectively then (p, q) = (1, -5).

Explanation:

y = px⁵ + qx⁴ + 5x³ - 10

`"dy"/"dx"` = 5px⁴ + 4qx³ + 15x² 

`=> ("dy"/"dx")_(x = 1)` = 5p + 4q + 15 = 0   ...(i)

and `("dy"/"dx")_(x = 3)` = 405p + 108q + 135 = 0

⇒ 15p + 4q + 5 = 0   ...(ii)

solving (i) and (ii), we get p = 1 and q = -5