Question

If f ( x ) = 4x² − 11x − 2 , find f ' ( x )?

a) f ′(x)=8x−11
b) f ′(x)=8x−11+2
c) f ′(x)=8x² - 11
d) f ′(x)=8x²−11x

Answer 1

The derivative of the function f(x) = 4x² − 11x − 2 is f '(x) = 8x − 11. We find this by applying the power rule to each term of the function, noting that the derivative of a constant is zero.

Step-by-step explanation:

To find f '(x) for the given function f(x) = 4x² − 11x − 2, we need to use the power rule of differentiation. The power rule states that if f(x) = ax^n, then f '(x) = n * ax^{n-1}. Applying this rule to each term in the function:

• The derivative of 4x² is 8x, because multiplying the exponent 2 by the coefficient 4 gives 8, and reducing the exponent by 1 gives us x.
• The derivative of − 11x is − 11, because the exponent of x is 1, and any number times 1 remains the same.
• The derivative of a constant, such as − 2, is 0. So, this term disappears in the derivative.

The derivative of the function f(x) = 4x² - 11x - 2 is f'(x) = 8x - 11.

To find the derivative, we use the power rule for differentiation. We bring down the exponent as the coefficient and then subtract 1 from the exponent: 2(4)x^(2-1) - 1(11)x^(1-1) - 0 = 8x - 11.

Therefore, the derivative of the function f(x) = 4x² − 11x − 2 is f '(x) = 8x − 11, which corresponds to option (a).