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Answered a Question in Math
f(x) is concave up
First derivative,
`f'(x) = 1*(x4)^3+x*3*1*(x4)^2`
`f'(x) = (x4)^2(x4+3x)`
... 
Answered a Question in Math
First derivative can be found using the quotient rule.
`f'(x) = ((x1)*1  x*x)/(x1)^2`
`f'(x) =...

Answered a Question in Math
First derivative,
`f'(x) = 1+4*(1)*x^(11) = 14x^2`
At critical points, `f'(x) = 0,`
`14/x^2 =...

Answered a Question in Math
First derivative,
`f'(x) = 1/2 * 2*x (x^2+1)^(1/21)`
`f'(x) = x(x^2+1)^(1/2)`
Therefore,...

Answered a Question in Math
First derivative,
`f'(x) = 2/3*x^(2/31) 0 = 2/3x^(1/3)`
At critical points, `f'(x) = 0`
... 
Answered a Question in Math
The first derivative,
`f'(x) = 4*x^34*3*x^2+0 = 4x^312x^2=4(x^33x^2)`
At critical points, `f'(x) = 0`
... 
Answered a Question in Math
First derivative to locate the x coordinates of critical points.
`f'(x) = 3*x^23*2*x+0 = 3x^26x `
At critical points,...

Answered a Question in Math
`f = x^2+3x8`
First derivative to find the locations of extreme points,
`f' = 2*x+30 = 2x+3`
At extremes...

Answered a Question in Math
`f = 6x x^2`
`f' = 62*x`
`f' = 2(3x)`
At extrema, f'=0, this give `3 x = 0 therefore x =3 `
At x = 3,...

Answered a Question in Math
See the attached MATLAB and it shows that there is a maximum and a minimum within that range.
We can find the x values of...