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Popular >

extreme y=(e^x)/(x^2-3x+2)

Solution

extreme points

y = \frac{e ^{x}}{x ^{2} - 3 x + 2}

Solution

Maximum (\frac{5 - 5}{2}, - e^{\frac{5 - 5}{2}} (5 + 2)), Minimum (\frac{5 + 5}{2}, e^{\frac{5 + 5}{2}} (5 - 2))

Solution steps

f^{'} (x) = \frac{e ^{x} x ^{2} - 5 e ^{x} x + 5 e ^{x}}{( x ^{2} - 3 x + 2 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < 1,

Increasing

: 1 < x < \frac{5 - 5}{2},

Decreasing

: \frac{5 - 5}{2} < x < 2,

Decreasing

: 2 < x < \frac{5 + 5}{2},

Increasing

: \frac{5 + 5}{2} < x < \infty

Plug

x = \frac{5 - 5}{2}

into

\frac{e ^{x}}{x ^{2} - 3 x + 2} : - e^{\frac{5 - 5}{2}} (5 + 2)

Maximum (\frac{5 - 5}{2}, - e^{\frac{5 - 5}{2}} (5 + 2))

Plug

x = \frac{5 + 5}{2}

into

\frac{e ^{x}}{x ^{2} - 3 x + 2} : e^{\frac{5 + 5}{2}} (5 - 2)

Minimum (\frac{5 + 5}{2}, e^{\frac{5 + 5}{2}} (5 - 2))

Maximum (\frac{5 - 5}{2}, - e^{\frac{5 - 5}{2}} (5 + 2)), Minimum (\frac{5 + 5}{2}, e^{\frac{5 + 5}{2}} (5 - 2))

Popular Examples

extreme g(t)=t^4+t^3+t^2+1 extreme points

g (t) = t^{4} + t^{3} + t^{2} + 1

extreme f(x,y)=(x+y)^3-12xy extreme points

f (x, y) = (x + y)^{3} - 12 x y

extreme f(x_{1},x_{2})=x_{1}+x_{1}x_{2}+x_{2}extreme points

f (x_{1}, x_{2}) = x_{1} + x_{1} x_{2} + x_{2}

extreme f(x)=-x^2+2x+6 extreme points

f (x) = - x^{2} + 2 x + 6

extreme f(x)=(x-2)^2-1 extreme points

f (x) = (x - 2)^{2} - 1

Frequently Asked Questions (FAQ)

What is the extreme y=(e^x)/(x^2-3x+2) ?
The extreme y=(e^x)/(x^2-3x+2) is