Increasing function's graph
\(f'(x)>0\)
\(f''(x)>0\)
\(f'(x)>0\)
\(f''(x)<0\)
Decreasing function's graph
\(f'(x)<0\)
\(f''(x)>0\)
\(f'(x)<0\)
\(f''(x)<0\)
1.
\(f:\mathbb R\to\mathbb R\)
\(y=f(x)=x^2-4x+7\)
\(\Rightarrow \min(y)=?\)
2.
\(f:\mathbb R\to\mathbb R\)
\(y=f(x)=-x^2+6x+17\)
\(\Rightarrow \max(y)=?\)
3.
\(f:\mathbb R\to\mathbb R\)
\(y=f(x)=3x^4-4x^3-6x^2+12x+9\)
\(\Rightarrow \min(y)=?\)
4.
\(f:\mathbb R\to\mathbb R\)
\(y=f(x)=3\cos x+4\sin x\)
\(\Rightarrow \max(y)=?\)
5.
\(f:\mathbb R\to\mathbb R\)
\(y=f(x)=3\sin x-2\cos x\)
\(\Rightarrow \min(y)=?\)
6.
\(f(x)=2x^3-3x^2+5\)
\(\Rightarrow(a,b)=?\)