`f(x) = sqrt(1 - x^3), (-2,3)` Find and evaluate the derivative of the function at the given point.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`f(x)=sqrt(1-x^3)`

`f'(x)=(1/2)(1-x^3)^(1/2-1)(-3x^2)`

`f'(x)=(-3x^2)/(2sqrt(1-x^3))`

Therefore the derivative of the function at the point (-2,3) can be obtained by plugging in the value of of x in the f'(x).

Derivative at point(-2,3)=`(-3(-2)^2)/(2sqrt(1-(-2)^3))`

Derivative at point (-2,3) = -2