Answer :
The function f(x) = 12x⁵+45x⁴-200x³+6 is increasing where its derivative f'(x) = 60x⁴+180x³-600x² is positive. Setting the derivative equal to zero, we find that it occurs for x>0. Hence, the function is increasing for x>0.
The subject of this question is in the field of Calculus, a branch of Mathematics. To find the intervals where the function is increasing for the given function f(x) = 12x⁵+45x⁴-200x³+6, we first need to find its derivative, f'(x), and find where this derivative is positive - this is because wherever the derivative is positive, the function is increasing.
The derivative f'(x) of the function is 60x⁴+180x³-600x², according to the power rule. Setting this derivative equal to zero and solving, we get x = 0 and a complex root which can be ignored in the real number space. This gives us the potential boundaries of intervals of increase.
Finally, we test the points in each interval against the derivative. This yields that f(x) is increasing for x>0.
The function f(x) = 12x⁵+45x⁴-200x³+6 is increasing for x>0.
Learn more about Finding Intervals of Increase here:
https://brainly.com/question/32846151
#SPJ11
