NDA2025MathematicsContinuity and DifferentiabilityActual

For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on the interval [0, 5] . What is dy dx at x = 3.5 equal to?

Options

A0
B1
C2
D3.5

Correct answer

A. 0

Step-by-step solution

Given f(x) = |x - 3| + |x - 4| on the interval [0, 5] . At x = 3.5 , we have 3 In the interval (3, 4) , x - 3 > 0 and x - 4 Therefore, f(x) = (x - 3) - (x - 4) = 1 . Since f(x) is a constant in the neighborhood of x = 3.5 , its derivative is zero. dy dx = 0 at x = 3.5 .

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