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

Expert Answers
Wilson2014 eNotes educator| Certified Educator

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.

pramodpandey | Student


`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)`



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