Question

14. Find the interval in which the function f(x) = 2x* - 15x + 36x +1 is strictly increasing and
strictly decreasing.​

Answer 1

Answer:

f(x) = 2x^3 - 15x^2 + 36x + 1

To check the intervals of monotonicity of the function in the domain of the function, we'll differentiate the function once with respect to variable x and then finally set it greater than or less than equal to zero except for critical points.

So,

f'(x) = 6x^2 - 30x + 36 = 6(x^2-5x+6) = 6(x-2)(x-3)

So, critical points of the graph are at x=2,3.

And,

The function is increasing in the interval

x € (-infinity , 2) U (3, infinity)

Since, (x-2)(x-3)>0 for these values of x

And, hence straight away

The function will be decreasing for the interval x € (2,3).

Since, there (x-2)(x-3)<0

Answer 2

Answer:

f(x) = 2x^3 - 15x^2 + 36x + 1

To check the intervals of monotonicity of the function in the domain of the function, we'll differentiate the function once with respect to variable x and then finally set it greater than or less than equal to zero except for critical points.

So,

f'(x) = 6x^2 - 30x + 36 = 6(x^2-5x+6) = 6(x-2)(x-3)

So, critical points of the graph are at x=2,3.

And,

The function is increasing in the interval

x € (-infinity , 2) U (3, infinity)

Since, (x-2)(x-3)>0 for these values of x

And, hence straight away

The function will be decreasing for the interval x € (2,3).

Since, there (x-2)(x-3)<0