2110013901 Level: AThe pictures show parts of graphs of functions that are increasing on the interval [1;5]. Choose the picture showing the part of the graph of the function f(x)=5x−1x+1.
2010017803 Level: ADetermine the values of a and b (a, b∈R) such that the function f(x)=ax3−2bx+2 has a local extremum of 6 at x=−1.a=2, b=3a=−2, b=3a=−2, b=−3a=2, b=−3
2010012505 Level: AIdentify a true statement about the function f(x)=−34x4+2x3.The function f has a local maximum at x=2.The function f has a local minimum at x=0.The function f has two local extrema. These extrema are at x=0 and x=2.The function f has neither local minimum nor local maximum.
2110012504 Level: BChoose the graph of a function f that satisfies f′(1) does not exist;f″(x)<0 if x<1;f″(x)<0 if x>2;f″(x)>0 if 1<x<2 (f′ is the derivative of a function f, f″ is the second derivative of a function f).
2110012503 Level: BChoose the graph of a function f that satisfies f′(−2)=f′(0)=0;f″(−2)<0; f″(0)>0 (f′ is the derivative of the function f, f″ is the second derivative of the function f).
2010001703 Level: AFind the intervals where the following function is an increasing function. f(x)=4+x2−4x[−2;0) and (0;2][−2;2](−∞;−2] and [2;∞)[2;∞)
2010001702 Level: AWhat is the function value of the function f at its local maximum? f(x)=6x−x223202The local maximum does not exist.
2010001701 Level: AFind all the x at which the function f has local extrema. f(x)=−2(x2−4)5x=0x1=0, x2=2x1=−2, x2=2x1=−2, x2=0, x3=2
1103163505 Level: BChoose the graph of a function f that satisfies f′(0) does not exist;f″(x)>0 if x<0;f″(x)>0 if x>1;f″(x)<0 if 0<x<1 (f′ is the derivative of a function f, f″ is the second derivative of a function f).