f(x) = x^2+(1000-x)^2
= 2x^2 - 2000x + 1000000
f' = 4x - 2000
f'=0 at x=500
f' < 0 for x < 500, so f is decreasing
f' > 0 for x > 500, so f is increasing
so, f(1000) > f(998) because f is increasing at that point
Hello! Really can't wrap my head around this so please help!
Consider the function:
f(x) = x^2+(1000-x)^2
First find out where it is increasing, and then use this fact to determine which number is larger:
a) 1000^2
or
b) 998^2 + 2^2
I found that the function increases at x=500 but how do I use that fact to figure this out???
2 answers
f(x) = x^2+(1000-x)^2
... = x² + 1E6 - 2000x + x²
... = 2x² - 2000x + 1E6
the minimum is on the axis of symmetry at x=500 ... the function increases from there
so as x increases (below x=500), the function decreases
f(0) = 0² + (1000 - 0)² = 1000²
f(2) = 2² + (1000 - 2)² = 998² + 2²
... = x² + 1E6 - 2000x + x²
... = 2x² - 2000x + 1E6
the minimum is on the axis of symmetry at x=500 ... the function increases from there
so as x increases (below x=500), the function decreases
f(0) = 0² + (1000 - 0)² = 1000²
f(2) = 2² + (1000 - 2)² = 998² + 2²
0 answers