Funksiyaning ekstremumlari mavzusidan test savollari

f(x)=3x-x^{3} funksiyaning maksimumini toping.

Ushbu g(x)=12x-x^{3} funksiyaning minimumini toping.

Ushbu y=\frac{x^{2}-2}{x+2} funksiyaning eng kichik qiymatini toping.

Ushbu f(x)=-\frac{2}{3}x^{3}+8x funksiyaning maksimumini toping.

Ushbu y=\frac{x^{2}-5}{x^{2}+5} funksiyaning eng kichik qiymatini toping.

Ushbu y=-4x^{3}+12x funksiyaning minimumini toping.

Ushbu y=x^{2}-8x+7 funksiyaning qiymatlari sohasini toping.

Ushbu y=x^{2}+8x+12 parabolaning uchi kordinatalar tekisligining qayerida yotadi.

Agar A(1;-2) nuqta y=x^{2}+px+q parabolaning uchi bo‘lsa, p va q ning qiymatini toping.

Ushbu f(x)=x^{3}+2.5x^{2}-2x funksiyaning maksimum nuqtasidagi qiymatini hisoblang.

Ushbu f(x)=\frac{x^{3}}{3}+\frac{x^{2}}{2}-6x funksiyaning maksimum nuqtasidagi qiymatini hisoblang.

t ning qanday qiymatida -t^{2}+14t-31 uchhad eng katta qiymatga erishadi?

Ushbu x^{2}-ax+a-1=0 tenglamaning ildizlari x_{1} va x_{2} bo‘lsin. a ning qanday qiymatida x_{1}^{2}+x_{2}^{2} yig‘indi eng kichik qiymatga ega bo‘ladi?

Ushbu f(x)=\frac{(x-1)^{2}+1}{x-1} funksiyaning minimum nuqtasidagi qiymatini toping.

Agar 2x+y=6 bo‘lsa, xy ning eng katta qiymati nechaga teng bo‘ladi?

y=-2x^{2}+2x+3 parabola uchining absissasini toping.

Ushbu y=-x^{2}+6x-8 funksiyaning eng katta qiymatini toping.

Ushbu y=\frac{2\cos ^{2}x+\sin 2x}{2\sin ^{2}x} funksiyaning eng kichik qiymatini toping.

Ifodaning eng katta qiymatini toping.

\frac{x^{2}+2x+8}{x^{2}+2x+3}

Agar a>0 bo‘lsa, y=x^{2}-2x-a parabolaning uchi koordinatalar tekisligining qaysi choragida joylashadi?

Ushbu y=-x^{2}+6x-12 funksiyaning qiymatlari sohasini toping.

Quyidagilardan qaysi biri y=\sqrt{x^{2}-6x+11} funksiyaning qiymatlar sohasi?

a ning qanday haqiqiy qiymatlarida x^{2}+ax+a-2=0 tenglama ildizlari kvadratlarining yig‘indisi eng kichik bo‘ladi?

Funksiyaning qiymatlar sohasini toping.

y=\sqrt{3x^{2}-4x+5}

Ushbu f(x)=\sqrt{2-x-x^{2}} funksiyaning eng katta qiymatini toping.

Ushbu y=\sqrt{3-x^{2}-2x} funksiyaning eng katta qiymatini toping.

Ushbu y=(\frac{1}{3})^{x^{2}-4x} funksiyaning eng katta qiymatini toping.

Ushbu y=(\sin \frac{\pi }{4})^{x^{2}-2x} funksiyaning eng katta qiymatini toping.

Ushbu f(x)=3^{1+x}+3^{1-x} funksiyaning eng kichik qiymatini toping.

Ushbu y=\sqrt{x^{2}-2x+10} funksiyaning qiymatlar sohasini toping.