# What is the slope of the line normal to the tangent line of #f(x) = x^2-3sqrtx # at # x= 3 #?

##### 1 Answer

#### Explanation:

Rewrite the square root:

Apply the power rule twice to find the first derivative of

Evaluating

The gradient product of two slant lines perpendicular to each other should equal to

Hence, the slope of the normal would equal to the opposite of the slope of the tangent inversed

#" "color(white)(l)=-1/(1/2*(12-sqrt(3)))#

Simplifying

#-1/(1/2*(12-sqrt(3)))#

#=2*1/(sqrt(3)-12)*color(grey)((sqrt(3)+12)/(sqrt(3)+12))#

#=-(24+2*sqrt(3))/(141)#