# Find the critical points a)h(x)=2x^3-23x^2-16x+1 b)h(x)=sqrt(1-7*x^2)

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a) You need to find the critical points of the given function `h(x) =`  `2x^3-23x^2-16x+1` , hence, you should find the roots of the equation `h'(x) = 0`  such that:

`h'(x) = (2x^3-23x^2-16x+1) => h'(x) = 6x^2 - 46x - 16`

You need to solve `h'(x) = 0`  such that:

`6x^2 - 46x - 16 = 0 => 3x^2 - 23x - 8 = 0`

`x_(1,2) = (23+-sqrt(23^2 - 4*3*(-8)))/(2*3)`

`x_(1,2) = (23+-sqrt(529+96))/6 => x_(1,2) = (23+-sqrt625)/6`

`x_(1,2) =...

(The entire section contains 231 words.)

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