Disguised problem!

Calculus Level 2

Let a function f f be defined as

f ( x ) = max ⁡ { x , − x } f(x) = \max \lbrace x, -x \rbrace

The distance of the point from origin where it is non-differentiable can be written as a b \displaystyle\frac{a}{b} .

Find the value of a b \displaystyle ab .

  • This is part of this set

  • This is original.


The answer is 0.

Gautam Sharma by Gautam Sharma , 23, India

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1 solution

Caleb Townsend
Mar 13, 2015

When x x is negative, f ( x ) = − x . f(x) = -x. When x x is nonnegative, f ( x ) = x . f(x) = x. This is the definition of f ( x ) = ∣ x ∣ f(x) = |x| So the non-differentiable point is ( 0 , 0 ) (0, 0) with a distance of 0 = a b 0 = \frac{a}{b} from the origin. Thus a = 0 a = 0 so a b = 0 ab = \boxed{0}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Perfectly undisguised it.Good solution.

Gautam Sharma - 6 years, 3 months ago

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