Question
Question: If f(x) = cos px + 10x + 3x<sup>2</sup> + x<sup>3</sup>, – 2 £ x £ 3 then absolute minimum value of ...
If f(x) = cos px + 10x + 3x2 + x3, – 2 £ x £ 3 then absolute minimum value of f(x) is-
A
0
B
–15
C
3 – 2p
D
None of these
Answer
–15
Explanation
Solution
f ¢(x) = –p sin px + 10 + 6x + 3x2
= 3x2 + 6x + 10 – p sin px
= 3(x + 1)2 + 7 – p sin x > 0 " x Î R
\ f(x) is monotonically increasing on [–2, 3]
Hence absolute minimum is f(–2) = –15