determine the value of a for which the function f has no critical number:
f(x)= (a^{2}+a-6)cos2x+(a-2)x+cos1
A root is a value that causes an expression to be zero. Anyway, consider:
Now, equate the second factor to zero, solve for and substitute into the above inequality. This will tell the the values of for which there are critical numbers.
When a=2, your function is constant, so there will be no critical values.
As for the second part, solve for sin(2x), then as an alternate to what I suggested before, set the magnitude of this to greater than 1. You will have 2 cases to consider:
i)
ii)