1.y=(a/b)^x乘以(b/x)^a乘以(x/a)^b,求导.2.求y=ax^2+bx+c上具有水平切线的点.3.写出y=x+1/x与X轴交点处的切线.
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1.y=(a/b)^x乘以(b/x)^a乘以(x/a)^b,求导.2.求y=ax^2+bx+c上具有水平切线的点.3.写出y=x+1/x与X轴交点处的切线.
1.y=(a/b)^x乘以(b/x)^a乘以(x/a)^b,求导.
2.求y=ax^2+bx+c上具有水平切线的点.
3.写出y=x+1/x与X轴交点处的切线.
1.y=(a/b)^x乘以(b/x)^a乘以(x/a)^b,求导.2.求y=ax^2+bx+c上具有水平切线的点.3.写出y=x+1/x与X轴交点处的切线.
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1、
y=(a/b)^x(b/x)^a(x/a)^b
=(b^a/a^b)[(a/b)^xx^(b-a)]
=(b^a/a^b)(a/b)^x[ln(a/b)x^(b-a)+(b-a)x^(b-a-1)]
2、
y'=0
2ax+b=0
x=-b/2a
y=b^2/4a-2b^2/4a+c
=-(b^2-4ac)/4a
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1、
y=(a/b)^x(b/x)^a(x/a)^b
=(b^a/a^b)[(a/b)^xx^(b-a)]
=(b^a/a^b)(a/b)^x[ln(a/b)x^(b-a)+(b-a)x^(b-a-1)]
2、
y'=0
2ax+b=0
x=-b/2a
y=b^2/4a-2b^2/4a+c
=-(b^2-4ac)/4a
该点坐标：(-b/2a,-(b^2-4ac)/4a)
3、
y'=1-1/x^2
y=0
x+1/x=0
x^2+1=0
x^2=-1
y'=0，切线就是x轴。该交点为虚交点。
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1,
y = (a/b)^x(b/x)^a(x/a)^b = [(a/b)^x][b^a]/[a^b][x^(b-a)]
= [b^a]/[a^b][x^(b-a)]e^[xln(a/b)]
y'= [b^a]/[a^b](b-a)[x^(b-a-1)]e^[xln(a/b)] + [b^a]/[a^b][x^(b-a)]e^[xln(a/b)][ln(a/b)]
...
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1,
y = (a/b)^x(b/x)^a(x/a)^b = [(a/b)^x][b^a]/[a^b][x^(b-a)]
= [b^a]/[a^b][x^(b-a)]e^[xln(a/b)]
y'= [b^a]/[a^b](b-a)[x^(b-a-1)]e^[xln(a/b)] + [b^a]/[a^b][x^(b-a)]e^[xln(a/b)][ln(a/b)]
= [b^a]/[a^b][x^(b-a-1)]e^[xln(a/b)][(b-a) + xln(a/b)]
2,
y = ax^2 + bx + c.
y' = 2ax + b = 0,
x = -b/(2a), y = a[-b/(2a)]^2 + b[-b/(2a)] + c = c - b^2/(4a).
y=ax^2+bx+c上具有水平切线的点的坐标为
(-b/(2a), c - b^2/(4a))
3,
y = x + 1/x,
y' = 1 - 1/x^2.
0 = x+1/x = (x^2 + 1)/x, 无解。
y = x+1/x与X轴没有交点。
若题目是，写出y=(x+1)/x与X轴交点处的切线.
则，
y = (x+1)/x = 1 + 1/x,
y' = -1/x^2.
0 = (x+1)/x, x = -1.
y'(-1) = -1/1 = -1.
y=(x+1)/x与X轴交点(-1,0)处的切线方程为，
y = -(x+1).
y + x + 1 = 0.
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