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Grade 12Algebra

If f is a real-valued differentiable function satisfying |f(x) – f(y)| = (x – y)2, x, y ? R and f(0) = 0, then f(1) equals ?

Profile image of sudhanshu
12 Years agoGrade 12
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1 Answer

Profile image of SHAIK AASIF AHAMED
12 Years ago
Hello student,
f′(x) =limh\rightarrow0 \frac{f(x+h)-f(x)}{h}
|f′(x)|=limh\rightarrow0 \frac{f(x+h)-f(x)}{h}\leq limh\rightarrow0\left | \frac{h^{2}}{h} \right |
⇒ |f′(x)| ≤ 0 ⇒ f′(x) = 0 ⇒ f(x) = constant
As f(0) = 0 ⇒ f(1) = 0.
Thanks and Regards
Shaik Aasif
askIITians faculty

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