Find the value of k for which the function f(x) = kx^2 + 3x + 2 is differentiabl
Practice Questions
Q1
Find the value of k for which the function f(x) = kx^2 + 3x + 2 is differentiable everywhere.
k = 0
k = -3
k = 1
k = 2
Questions & Step-by-Step Solutions
Find the value of k for which the function f(x) = kx^2 + 3x + 2 is differentiable everywhere.
Correct Answer: Any real number
Step 1: Understand what it means for a function to be differentiable. A function is differentiable everywhere if it has a derivative at every point in its domain.
Step 2: Identify the type of function given. The function f(x) = kx^2 + 3x + 2 is a polynomial function.
Step 3: Recall the properties of polynomial functions. Polynomial functions are smooth and continuous, which means they are differentiable everywhere.
Step 4: Conclude that since f(x) is a polynomial, it does not depend on the value of k for differentiability.
Step 5: State that k can be any real number because the function will still be differentiable for all values of k.
Differentiability of Polynomials – Polynomials are differentiable everywhere on the real number line, meaning they do not have any points of non-differentiability.
