Question

The values of x at which the real valued function $f(x)=7|2x+1|-19|3x-5|$ is not differentiable is

• A. 1, -1
• B. $\frac{1}{2}, \frac{5}{3}$
• C. $-\frac{1}{2}, \frac{5}{3}$
• D. 0, 1

Hint:

To quickly find the points where a function involving absolute values is not differentiable, set the expression inside each absolute value to zero and solve for $x$. These points are the "critical points" where the function's definition changes, leading to sharp corners in the graph.

Answer 1

The Correct Option is C

Step 1: Concept of Differentiability for Modulus: The function \( |ax+b| \) is continuous everywhere but non-differentiable at the point where the argument is zero, i.e., \( x = -b/a \).
Step 2: Find critical points: For \( |2x+1| \), non-differentiable at \( 2x+1=0 \implies x = -1/2 \). For \( |3x-5| \), non-differentiable at \( 3x-5=0 \implies x = 5/3 \).
Step 3: Conclusion: The function is not differentiable at \( x = -1/2 \) and \( x = 5/3 \). (Matches Option C accounting for standard format).