Question
Download Solution PDF(1, 1) पर वक्र y = x3 की स्पर्शरेखा का समीकरण क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
एक बिंदु (a, b) पर वक्र y = f(x) की स्पर्शरेखा का समीकरण (y - b) = m(x - a) द्वारा दिया जाता है, जहाँ m = y'(b) = f'(a) [बिंदु (a, b) पर अवकलज का मूल्य]।
गणना:
y = f(x) = x3
⇒ y' = f'(x) = 3x2
m = f'(1) = 3 × 12 = 3
(1, 1) पर स्पर्शरेखा का समीकरण होगा:
(y - b) = m(x - a)
⇒ (y - 1) = 3(x - 1)
⇒ y - 1 = 3x - 3
⇒ 3x - y - 2 = 0.
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