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If (f:[0,\frac{\pi}{2}]\to\mathbb{R}), (f(x)=\sin x+\cos x), on which subinterval is (f) one-one?यदि (f:[0,\frac{\pi}{2}]\to\mathbb{R}), (f(x)=\sin x+\cos x) है, तो (f) किस उपअंतराल पर एकैकी है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \([0,\frac{\pi}{4}]\) / ([0,\frac{\pi}{4}])\([0,\frac{\pi}{4}]\) / ([0,\frac{\pi}{4}])
Step 1: (f'(x)=\cos x-\sin x). Step 2: On ([0,\frac{\pi}{4}]), (f'(x)\ge0), so the function is increasing and one-one. Step 3: When the derivative changes sign, choose a monotonic part.चरण 1: (f'(x)=\cos x-\sin x) है। चरण 2: ([0,\frac{\pi}{4}]) पर (f'(x)\ge0), इसलिए फलन बढ़ता है और एकैकी है। चरण 3: जब अवकलज का संकेत बदलता हो, तो केवल एकरस भाग चुनें।
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