Question

Compare the following functions:

Answer 1

Which function has the smallest minimum?
All three functions have the same minimum

f(x)

g(x)

h(x)

Answer 2

@M4thM1nd

Answer 3

Ok, let's check first the g(x), it's a quadratic equation with minimum at (3,-2)

Answer 4

okay

Answer 5

now function f(x) = -5*sin(2x-pi)+2
let's take the first derivative and find it's roots
f'(x) = -10*cos(2x-pi)

Answer 6

okayayay

Answer 7

-10*cos(2x-pi) = 0
cos(2x-pi) = 0
2x-pi = acos(0) = pi/2 + n*pi, n is a integer

Answer 8

2x = 3*pi/2 + n*pi
2x = (3/2 + n)*pi
x = (3/4 + N)*pi
so let's try N = 0
x = (3/4)*pi

Answer 9

that is a minimum

Answer 10

@larryboxaplenty

Answer 11

okay :)

Answer 12

The minimum for f(x) looks like -3

Answer 13

so the answer would be f(x) right?

Answer 14

minimum for g(x) is -2
minimum for h(x) is between 3 and 5

Answer 15

yup so it's f(x). thank you!

Answer 16

right...?

Answer 17

I graphed f(x), so yes, it looks like it has the lowest min

Answer 18

You were right! Thank you so much :))))

Answer 19

yes f(x) at it's minimum is -3, the h(x) we know that the minimum is somewhere between x = 1 and x = 2, you could make a lagrange interpolation of this table and make a better view of this data distribution