Question

Find the derivative of f(x) = -4x^2 + 11x at x = 10.

a. -69
b. -49
c. -29
d. -9

Answer 1

The derivative of f(x) = -4x^2 + 11x is found by applying the power rule, resulting in f'(x) = -8x + 11. Substituting x = 10 gives f'(10) = -69.

Step-by-step explanation:

To find the derivative of the function f(x) = -4x^2 + 11x at x = 10, we first need to apply basic differentiation rules.

Using the power rule, which states that the derivative of x^n is nx^(n-1), we differentiate each term of the function separately:

• The derivative of -4x^2 is -8x.
• The derivative of 11x is 11.

Therefore, the derivative of f(x) is f'(x) = -8x + 11. To find the value of this derivative at x = 10, we simply substitute 10 into the derivative:

f'(10) = -8(10) + 11 = -80 + 11 = -69.

The correct answer is a. -69.