Answer: bellow !
Explanation:
To find the derivative of the function f(x) = (1/3)x^4 + (3/2) and evaluate it at x = -3, we can follow these steps:
Step 1: Differentiate each term of the function separately.
The derivative of (1/3)x^4 with respect to x is (4/3)x^3.
The derivative of (3/2) with respect to x is 0, since it is a constant term.
Step 2: Simplify the derivative by combining like terms.
The derivative of f(x) is therefore (4/3)x^3.
Step 3: Evaluate the derivative at x = -3.
To find f'(-3), we substitute -3 into the derivative we just found:
f'(-3) = (4/3)(-3)^3
= (4/3)(-27)
= -36
Therefore, the derivative of f(x) = (1/3)x^4 + (3/2) at the point x = -3 is f'(-3) = -36.