4.2-bo'lim : Muhim nuqtalar
1 - 43 muammolar uchun quyidagi funktsiyalarning har birining kritik nuqtalarini aniqlang. E'tibor bering, bir nechta muammolar qo'lda osonlikcha yechilmaydigan tenglamalarni o'z ichiga oladi va shuning uchun ba'zi hisoblash vositalarini talab qilishi mumkin. Bu belgilar quyida qayd etilgan.
- \(R\left( x \right) = 8{x^3} - 18{x^2} - 240x + 2\)
- \(f\left( z \right) = 2{z^4} - 16{z^3} + 20{z^2} - 7\)
- \(\displaystyle g\left( z \right) = 8 - 12{z^5} - 25{z^6} + \frac{90}{7}{z^7}\)
- \(g\left( t \right) = 3{t^4} - 20{t^3} - 132{t^2} + 672t - 4\)
Eslatma: Faktoring qobiliyatingizga qarab, bu ba'zi hisoblash vositalarini talab qilishi mumkin. - \(\displaystyle h\left( x \right) = 10{x^2} - 15{x^3} + \frac{15}{2}{x^4} - {x^5}\)
Eslatma: Faktoring qobiliyatingizga qarab, bu ba'zi hisoblash vositalarini talab qilishi mumkin. - \(P\left( w \right) = {w^3} - 4{w^2} - 7w - 1\)
- \(A\left( t \right) = 7{t^3} - 3{t^2} + t - 15\)
- \(a\left( t \right) = 4 - 2{t^2} - 6{t^3} - 3{t^4}\)
- \(f\left( x \right) = 3{x^4} - 20{x^3} + 6{x^2} + 120x + 5\)
Eslatma: Faktoring qobiliyatingizga qarab, bu ba'zi hisoblash vositalarini talab qilishi mumkin. - \(h\left( v \right) = {v^5} + {v^4} + 10{v^3} - 15\)
- \(g\left( z \right) = {\left( {z - 3} \right)^5}{\left( {2z + 1} \right)^4}\)
- \(R\left( q \right) = {\left( {q + 2} \right)^4}{\left( {{q^2} - 8} \right)^2}\)
- \(f\left( t \right) = {\left( {t - 2} \right)^3}{\left( {{t^2} + 1} \right)^2}\)
- \(\displaystyle f\left( w \right) = \frac{{{w^2} + 2w + 1}}{{3w - 5}}\)
- \(\displaystyle h\left( t \right) = \frac{{3 - 4t}}{{{t^2} + 1}}\)
- \(\displaystyle R\left( y \right) = \frac{{{y^2} - y}}{{{y^2} + 3y + 8}}\)
- \(Y\left( x \right) = \sqrt[3]{{x - 7}}\)
- \(f\left( t \right) = {\left( {{t^3} - 25t} \right)^{\frac{2}{3}}}\)
- \(h\left( x \right) = \sqrt[5]{x}\,\,{\left( {2x + 8} \right)^2}\)
- \(Q\left( w \right) = \left( {6 - {w^2}} \right)\,\,\,\sqrt[3]{{{w^2} - 4}}\)
- \(\displaystyle Q\left( t \right) = 7\sin \left( \frac{t}{4} \right) - 2\)
- \(g\left( x \right) = 3\cos \left( {2x} \right) - 5x\)
- \(f\left( x \right) = 7\cos \left( x \right) + 2x\)
- \(h\left( t \right) = 6\sin \left( {2t} \right) + 12t\)
- \(\displaystyle w\left( z \right) = {\cos ^3}\left( \frac{z}{5} \right)\)
- \(U\left( z \right) = \tan \left( z \right) - 4z\)
- \(h\left( x \right) = x\cos \left( x \right) - \sin \left( x \right)\)
- \(h\left( x \right) = 2\cos \left( x \right) - \cos \left( {2x} \right)\)
- \(f\left( w \right) = {\cos ^2}\left( w \right) - {\cos ^4}\left( w \right)\)
- \(F\left( w \right) = {{\bf{e}}^{14w + 3}}\)
- \(g\left( z \right) = {z^2}{{\bf{e}}^{1 - z}}\)
- \(A\left( x \right) = \left( {3 - 2x} \right){{\bf{e}}^{{x^{\,2}}}}\)
- \(P\left( t \right) = \left( {6t + 1} \right){{\bf{e}}^{8t - {t^{\,2}}}}\)
- \(f\left( x \right) = {{\bf{e}}^{3 + {x^{\,2}}}} - {{\bf{e}}^{2{x^{\,2}} - 4}}\)
- \(f\left( z \right) = {{\bf{e}}^{{z^{\,2}} - 4z}} + {{\bf{e}}^{8z - 2{z^2}}}\)
- \(h\left( y \right) = {{\bf{e}}^{6{y^{\,3}} - 8{y^{\,2}}}}\)
- \(g\left( t \right) = {{\bf{e}}^{2{t^{\,3}} + 4{t^{\,2}} - t}}\)
- \(Z\left( t \right) = \ln \left( {{t^2} + t + 3} \right)\)
- \(G\left( r \right) = r - \ln \left( {{r^2} + 1} \right)\)
- \(A\left( z \right) = 2 - 6z + \ln \left( {8z + 1} \right)\)
- \(f\left( x \right) = x - 4\ln \left( {{x^2} + x + 2} \right)\)
- \(g\left( x \right) = \ln \left( {4x + 2} \right) - \ln \left( {x + 4} \right)\)
- \(h\left( t \right) = \ln \left( {{t^2} - t + 1} \right) + \ln \left( {4 - t} \right)\)
- Ba'zi funksiyalarning grafigi \(f\left( x \right)\) ko'rsatilgan. Grafikga asoslanib, funktsiyaning barcha kritik nuqtalarining joylashishini taxmin qiling.
- Ba'zi funksiyalarning grafigi, \(f\left( x \right)\) ko'rsatilgan. Grafikga asoslanib, funktsiyaning barcha kritik nuqtalarining joylashishini taxmin qiling.
- Ba'zi funksiyalarning grafigi \(f\left( x \right)\) ko'rsatilgan. Grafikga asoslanib, funktsiyaning barcha kritik nuqtalarining joylashishini taxmin qiling.
