Asosiy tarkibga o'tish

3.2-bo'lim : Hosilaning talqini

4. \(f\left( { - 3} \right) = 5\), \(f'\left( { - 3} \right) = - 2\), \(f\left( 1 \right) = 2\), \(f'\left( 1 \right) = 0\), \(f\left( 4 \right) = - 2\), \(f'\left( 4 \right) = - 3\) 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 three given points and the tangent lines at those points. The point \(\left( { - 3,5} \right)\) has a short line through it falling to the right with a slope of -2, the point \(\left( {1,2} \right)\) has a short horizontal line through it since the slope there is 0, and the point \(\left( {4, - 2} \right)\) has a short line through it falling steeply to the right with a slope of -3.
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 three points and their tangent lines. The curve comes down from the upper left through \(\left( { - 3,5} \right)\) parallel to the falling tangent line there, flattens out and just touches the horizontal tangent line as it passes through \(\left( {1,2} \right)\), and then falls away steeply through \(\left( {4, - 2} \right)\) parallel to the 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 comes down from the upper left, flattens out into a nearly level stretch at about \(y = 2\) between \(x = 0\) and \(x = 2\), and then falls away steeply, crossing the x-axis near \(x = 3\) and continuing down to the lower right.