Question

What is that is the derivative of

x^2-x+3 at the point
x=5
What value of x where
x²-x+3
a minimum?
​

Answer 1

see explanation

Explanation:

differentiate using the power rule.

`(d)/(dx)`( a
`x^(n)` ) = na
`x^(n-1)` , thus

`(d)/(dx)`(x² - x + 3 ) = 2x - 1

x = 5 → 2(5) - 1 = 10 - 1 = 9

To find the value of x for minimum , equate
`(d)/(dx)` to zero

2x - 1 = 0 , then

2x = 1 and

x =
`(1)/(2)`