Asosiy tarkibga o'tish

3.2-bo'lim : Hosilaning talqini

3. \(f\left( 1 \right) = 3\), \(f'\left( 1 \right) = 1\), \(f\left( 4 \right) = 5\), \(f'\left( 4 \right) = - 2\) ni qanoatlantiradigan funksiya grafigini chizing.

Yechim

Birinchidan, lotinning talqinlaridan biri shuni esda tutingki, u ma'lum bir nuqtadagi funktsiyaga teginish chizig'ining qiyaligidir. Shunday qilib, keling, berilgan nuqtalari bo'lgan grafikdan va qiyaliklari nuqtalardagi hosilaning qiymati bo'lgan nuqtalardagi tangens chiziqning eskizidan boshlaylik.

A sketch showing just the two given points and the tangent lines at those points. The point \(\left( {1,3} \right)\) is marked with a dot and has a short line through it rising to the right with a slope of 1, and the point \(\left( {4,5} \right)\) is marked with a dot and has a short line through it falling to the right with a slope of -2.
2-qadam

Endi biz qilishimiz kerak bo'lgan narsa - ko'rsatilgan nuqtalardan o'tadigan grafikda eskiz qilish va shu bilan birga u biz chizgan tangenslarga parallel bo'lishi kerak. Biz bu yerda yaratishimiz mumkin bo'lgan ko'plab eskizlar mavjud va shuning uchun sizning eskizingiz bu yerdagi bilan bir xil bo'lmasa, tashvishlanmang. Bu berilgan shartlarga javob beradigan bitta mumkin bo'lgan eskiz.

A sketch of a function that satisfies the given conditions, drawn in with the two points and their tangent lines. The curve passes through \(\left( {1,3} \right)\) rising and parallel to the tangent line there, continues up to a peak between \(x = 3\) and \(x = 4\), and then comes back down through \(\left( {4,5} \right)\) parallel to the falling tangent line there.

Garchi bu erda funksiyaning eskizi kerak bo'lmasa-da, biz eskizda yordam berish uchun qo'shadigan barcha qo'shimcha bitlarsiz.

A sketch of a function that satisfies the given conditions with the points and tangent lines removed. The curve starts near \(\left( {0,3} \right)\), dips to a shallow valley just after that, rises through \(\left( {1,3} \right)\) up to a peak near \(x = 3.3\) and then falls off to about \(\left( {5,1} \right)\) at the right end.