Absolute maximum value of the function (x^2 – 2x + 7)e^(4x^3 – 12x^2 – 180x + 31)

If the absolute maximum value of the function

, then

1. 
2. 
3. 
4. 

Solution:

Tip for solving this question:

Find differentiation of f(x)

The absolute maximum value of x

Step 1 of 2:

Given,

Take

Now, differentiate

For critical points,

Here,

From the above values, we see that the absolute maximum is 22

and it occur at x = -3.

Here, is decreasing in [-3, 0] and positive.

Now, differentiate

For critical points,

Here,

The above values show that the absolute maximum is 3.08, and it occurs at x = -3.

Here, is decreasing in [-3, 0] and positive.

Step 2 of 2:

Both decreasing in [-3, 0] and positive.

i.e. f(x) is decreasing in [-3, 0] and positive.

Therefore, Absolute maximum value of f(x) occurs at x = -3

So,

Final Answer:

Hence, Option (B) is correct.