Question

Show the function f of x is equal to x cube minus 3 x square + 6 x minus under increasing or not

Answer 1

Answer:

x³ - 3x² + 6x - 100 is  an increasing function

Step-by-step explanation:

Show the function f of x is equal to x cube minus 3 x square + 6 x minus 100 increasing or not

x³ - 3x² + 6x - 100

f(x) = x³ - 3x² + 6x - 100

f(x+1) = (x+1)³ -3(x+1)² + 6(x+1) - 100

f(x+1)= x³ + 1 + 3x² + 3x - 3(x² + 1 + 2x) + 6x + 6 - 100

f(x+1)= x³ - 3x² + 6x - 100 + (3x² -3x + 4)

f(x+1) - f(x) = 3x² - 3x + 4

= 3x² - 3x + 3/4  + 13/4

= 3(x² - x  + 1/4) + 13/4

= 3(x- 1/2)² + 13/4

as (x- 1/2)² ≥ 0

so 3(x- 1/2)² + 13/4 ≥ 13/4 > 0

so we can say function is increasing