Answer:
Range: 1 > x > 3
Explanation:
We are given then function;
y = x³ - 6x² + 9x + 5
dy/dx = 3x² - 12x + 9
We want to find the range of values of x for which dy/dx > 0
Thus;
3x² - 12x + 9 > 0
Using quadratic formula, we have;
x = 1 and x = 3
Let's define the range;
try x = 0
3(0²) - 12(0) + 9 = 9
This is more than 0, so it is part of the solution.
Let's try x = 4
3(4²) - 12(4) + 9 = 9
This is more than 0 so it is part of the solution
Let's try x = 2
3(2²) - 12(2) + 9 = -3
This is less than 9 and so it's not part of the solution.
Thus the range of values of x for which dy/dx > 0 is;
1 > x > 3