Question

If g(x) = x²/2 - 4x then g ′(x) is equal to which of the following?

a) x² - 4
b) x² - 4x
c) x - 4
d) x - 2

Answer 1

The first derivative of the function g(x) = x²/2 - 4x is g ′(x) = x - 4, which is option (d).

Step-by-step explanation:

The question involves finding the first derivative of the function g(x) = x²/2 - 4x. To find the derivative, g ′(x), we need to apply the power rule of differentiation. The power rule states that if you have a function of the form f(x) = x^n, its derivative f ′(x) is nx^(n-1). Applying this to each term of g(x), we get:

• The derivative of x²/2 with respect to x is (2/2)x^(2-1) = x
• The derivative of -4x with respect to x is -4

Combining these results, we get g ′(x) = x - 4, which corresponds to option (d).