The equation of a straight line is determined by computing its #color(red)(slope) # and the point it passes through name it #(color(purple)(x_1,y_1))#
This line is normal to #f(x)# at #color(purple)(x=-5)# so it passes through the point#(color(purple)(-5,f(-5)))#
#color(purple)(f(-5))=(-5)^2=25#
This line passes through the point #(color(purple)(-5,25))#
The #color(red)(slope) # at #x=-5# is determined by computing #color(red)(f'(-5))#
#f(x)# is differentiated by using power rule differentiation
#(x^n)'=n(x^(n-1))#
#f'(x)=2x#
# color(red)(f'(-5)=2(-5)=-10)#
The equation is:
#y-y_1=color(red)(slope)(x-x_1)#
#y-f(-5)=-10(x-(-5))#
#y-25=-10(x+5)#
#y=-10x-50+25#
#y=-10x-25#
