The derivative of the function y = f (x) has the form f ‘(x) = 4x-23. find the point where the function takes the smallest value.

Let’s find the derivative of our given function: f (x) = (3 – 4x) ^ 3.

Using the basic formulas and rules of differentiation:

(x ^ n) ‘= n * x ^ (n-1).

(c) ‘= 0, where c is const.

(c * u) ’= c * u’, where c is const.

(u ± v) ‘= u’ ± v ‘.

y = f (g (x)), y ‘= f’u (u) * g’x (x), where u = g (x).

Thus, the derivative of our given function will be as follows:

f (x) ‘= ((3 – 4x) ^ 3)’ = (3 – 4x) ‘* ((3 – 4x) ^ 3)’ = ((3) ‘- (4x)’) * ((3 – 4x) ^ 3) ‘= (0 – 4) * 3 * (3 – 4x) ^ 2 = -4 * 3 * (3 – 4x) ^ 2 = -12 * (3 – 4x) ^ 2 = -12 (3 – 4x) ^ 2.

Answer: The derivative of our given function will be equal to f (x) ‘= -12 (3 – 4x) ^ 2.