4.7-bo'lim: O'rtacha qiymat teoremasi

1 va 2-masalalar uchun berilgan funksiya va interval uchun Rol teoremasining xulosasini qanoatlantiradigan barcha c son(lar)ni aniqlang.

1. \(f\left( x \right) = {x^2} - 2x - 8\) on \(\left[ { - 1,3} \right]\) Yechim
2. \(g\left( t \right) = 2t - {t^2} - {t^3}\) on \(\left[ { - 2,1} \right]\) Yechim

3 va 4-masalalar uchun berilgan funksiya va interval uchun oʻrtacha qiymat teoremasining xulosasini qanoatlantiradigan barcha c son(lar)ni aniqlang.

1. \(h\left( z \right) = 4{z^3} - 8{z^2} + 7z - 2\) on \(\left[ {2,5} \right]\) Yechim
2. \(A\left( t \right) = 8t + {{\bf{e}}^{ - 3\,t}}\) on \(\left[ { - 2,3} \right]\) Yechim
3. Faraz qilaylik, biz \(f\left( x \right)\) uzluksiz va \(\left[ { - 7,0} \right]\), bu \(f\left( { - 7} \right) = - 3\) va \(f'\left( x \right) \le 2\) oralig‘ida differensiallanuvchi ekanligini bilamiz. \(f\left( 0 \right)\) uchun mumkin bo'lgan eng katta qiymat nima? Yechim
4. \(f\left( x \right) = {x^3} - 7{x^2} + 25x + 8\) aynan bitta haqiqiy ildizga ega ekanligini ko'rsating. Yechim