Evaluate the derivative of yx33 2sqrtx for x3SolutionWell c

Evaluate the derivative of y=x^3/3 - 2sqrtx for x=3

Solution

We\'ll calculate the expression of derivative of y.

We\'ll note f(x) = y.

f\'(x) = (x^3/3 - 2sqrtx)\'

f\'(x) = 3x^2/3 - 2/2sqrtx

We\'ll simplify f\'(x):

f\'(x) = x^2 - 1/sqrtx

We\'ll substitute x by 3 and we\'ll get:

f\'(3) = 3^2 - 1/sqrt3

f\'(3) = 9 - 1/sqrt3

Another method is to calculate the limit of the ratio:

lim [f(x) - f(3)/(x-3)],when x->3