Find the value of k such that the function f(x) = x^2 + kx has a maximum at x =
Practice Questions
Q1
Find the value of k such that the function f(x) = x^2 + kx has a maximum at x = -2.
-4
-2
0
2
Questions & Step-by-Step Solutions
Find the value of k such that the function f(x) = x^2 + kx has a maximum at x = -2.
Step 1: Start with the function f(x) = x^2 + kx.
Step 2: To find the maximum, we need to find the derivative of f(x). The derivative f'(x) is calculated as f'(x) = 2x + k.
Step 3: We want to find the value of k such that the maximum occurs at x = -2.
Step 4: Substitute x = -2 into the derivative: f'(-2) = 2(-2) + k.
Step 5: Simplify the equation: f'(-2) = -4 + k.
Step 6: For a maximum, the derivative must equal 0. So, set -4 + k = 0.
Step 7: Solve for k: k = 4.
Derivative and Critical Points – Understanding how to find critical points of a function using its derivative to determine maxima and minima.
Quadratic Functions – Recognizing the properties of quadratic functions, particularly how the coefficients affect the shape and position of the parabola.
