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3 solutions
Your third step is incorrect , it should be
f ′ ( x ) = ∣ x − 1 ∣ x − 1 + ∣ x − 3 ∣ x − 3
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Whats the big difference between that and what i wrote? It's all same.
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No your answer came correct but it will be 4-1/4-1 + 4-3/4-3 =2. Yiur answer is correct but you have dine it wron brother
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@Md Zuhair – It's actually correct. View wiki of modulus or absolute derivative
What is the proof that d x d ∣ x ∣ = x ∣ x ∣ ?
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As |x|=y . By squaring and differentuating we get dy/dx = x ∣ x ∣
Wrong. It will be x − 3 ∣ x − 3 ∣ will be the 1st expressions derivative
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The derivative of an absolute or a modulus gives the absolute integer form of the number, ie +1 or -1
Let's consider x is greater than 3 so equation becomes y=2x -3 simply slope is 2
∀ x > 3 f ( x ) = 2 x − 4 ⇒ f ′ ( 4 ) = 2
d x d ∣ x ∣ = x ∣ x ∣ f ( x ) = ∣ x − 1 ∣ + ∣ x − 3 ∣ f ′ ( x ) = x ∣ x ∣ + x ∣ x ∣ f ′ ( 4 ) = 4 ∣ 4 ∣ + 4 ∣ 4 ∣ = 1 + 1 = 2