Assertion : \) If =|x|, \) then has minimum value at Reason (R): A function f(x) has minimum value at if =0 \) and >\mathbf{0} \)

Both A and R are true and R is not the correct explanation of A

Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable

Assertion : \) If =|x|, \) then has minimum value at Reason (R): A function f(x)

Assertion \( (A): \) If \( f(x)=|x|, \) then \( f \) has minimum value at \( x=0 \) Reason (R): A function f(x) has minimum value at \( x=a \) if \( f^{\prime}(a)=0 \) and \( \mathbf{f}^{\prime \prime}(\mathbf{a})>\mathbf{0} \)

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of A
C. A is true and R is false
D. A is false and R is true

Step-by-step solution

Assertion A is true because f(x)=|x| has a minimum value of 0 at x=0. Reason R states a sufficient condition for a minimum (f'(a)=0 and f''(a)>0), which is true in general, but it does not apply to f(x)=|x| since the function is not differentiable at x=0. Hence R is not the correct explanation for A.

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Step-by-step solution

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