Question

Find the maximum value of the polynomial -2x^4+7x^2+5​

Answer 1

differentiate this polynomial

f '(x) = -8x^3 + 14x

on maximum and minimum value of a function f(x), f '(x) = 0

so, -8x^3 + 14x = 0

=> x (14 - 8x^2) = 0

so, x = 0 , x = √7/2 and -√7/2

and when f ''(x) < 0 , the value on x is maximum and f ''(x) > 0, the value on x is minimum

so f ''(x) = -24x^2 + 14

when x = √7/2 and -√7/2 , f ''(x) is -24*7/4 + 14 which is negative

and when x = 0 , f "(x) > 0

so the polynomial has maximum value on x = √7/2 and -√7/2

so, the value is 2*49/16 + 7*7/4 + 5

= 187/8. Ans.