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Locate all critical points (both types) of `h(x)= sqrt(1-7x^2)` The critical points are:

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elpony | Student, Undergraduate | (Level 1) Honors

Posted April 23, 2013 at 3:33 AM via web

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Locate all critical points (both types) of `h(x)= sqrt(1-7x^2)`

The critical points are:

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Wilson2014 | eNotes Employee

Posted April 25, 2013 at 10:01 PM (Answer #2)

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Other critical points are the x-values that make the `(1/(2*sqrt (1-7x)^2)` undefined. Solving for x, we will get `x = +-sqrt (1/7)`. So, `+-sqrt (1/7)` are additional critical points.

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted April 23, 2013 at 4:58 AM (Answer #1)

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`h(x)=sqrt(1-7x^2)`      (i)

Differentiate  (i) ,with respect to x

`h'(x)=(1/(2sqrt(1-7x^2)))(-14x)`     (ii)

`h'(x)=0 if x=0`

Differentate (ii) with respect to x

`h''(x)={-7(sqrt(1-7x^2)-xd/(dx)(sqrt(1-7x^2))) } /(1-7x^2)`

``

`h''(x)}_{x=0}=-7<0`

`` Thus    x=0 is a critical point and it is point of maxima.

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