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Popular >

extreme e^{3x^2-x-3}

Solution

extreme points

e^{3 x^{2} - x - 3}

Solution

Minimum (\frac{1}{6}, \frac{1}{e ^{\frac{37}{12}}})

Solution steps

f^{'} (x) = e^{3 x^{2} - x - 3} (6 x - 1)

Find intervals:

Decreasing

: - \infty < x < \frac{1}{6},

Increasing

: \frac{1}{6} < x < \infty

Plug

x = \frac{1}{6}

into

e^{3 x^{2} - x - 3} : \frac{1}{e ^{\frac{37}{12}}}

Minimum (\frac{1}{6}, \frac{1}{e ^{\frac{37}{12}}})

Graph

Popular Examples

extreme f(x)=-2x^3+18x^2-30x,0<= x<= 6 extreme points

f (x) = - 2 x^{3} + 18 x^{2} - 30 x, 0 \leq x \leq 6

extreme f(x)=3sqrt(3)x+6cos(x)extreme points

f (x) = 33 x + 6 cos (x)

extreme f(x)=f(x,y)=2y^2+2xy+x^2-16x-20y extreme points

f (x) = f (x, y) = 2 y^{2} + 2 x y + x^{2} - 16 x - 20 y

extreme f(x)=x(20-39+2x)(39/2-x)extreme points

f (x) = x (20 - 39 + 2 x) (\frac{39}{2} - x)

extreme (x^2+1)/(x^2-9)extreme points

\frac{x ^{2} + 1}{x ^{2} - 9}

Frequently Asked Questions (FAQ)

What is the extreme e^{3x^2-x-3} ?
The extreme e^{3x^2-x-3} is Minimum(1/6 , 1/(e^{37/12)})