Question

Which function has a greater minimum?
f(x)=4(x-5)^2+2

Answer 1

The parabola minimum is 3

The top quadratic minimum is 2 so

g(x) minimum is greater

Explanation:

Answer 2

The answer is "-2".

Explanation:

Given value:

`f(x) = 4(x-5)^2+2\\\\`

`\ formula: \\\\(a-b)^2 = a^2+b^2-2ab\\\\`

`\ f(x) = 4( x^2+5^2-2 * 5 * x) +2\\\\\ f(x) = 4(x^2+25-10x)+2\\\\\ f(x) = 4x^2+100-40x+2\\\\\ f(x) = 4x^2-40x+98\\\\`

taking derivative of the above function two times:

`f (x)' = 8x-40\\\\f (x)'' = 8 \\\\`

let first derivative equal to 0.

`8x-40 =0\\\\8x= 40\\\\x= (40)/(8)\\\\x= 5\\\\\ put \ the \ value \ of\ x \ in \ f(x)\ function :\\\\ f(x) = 4 (5)^2-40 (5)+98\\\\f(x)= 4 * 25 - 40 * 5 +98\\\\f(x) = 100-200+98\\\\f(x) = -100+98\\\\f(x) -2`

The greatest minimum value is -2.