# Normal Line to a Tangent

Understanding the transition from a normal line to a tangent is pivotal in calculus and geometry. The normal line, perpendicular to a curve at a specific point, provides a fundamental reference. As we delve into the intricacies of this transition, the concept of a tangent emerges—an instantaneous approximation of the curve's behavior at that point. This shift from perpendicularity to tangency elucidates the dynamic relationship between a curve and its tangent, forming the basis for differential calculus. Exploring this connection unveils the profound significance of the normal line as a precursor to the nuanced understanding of curves and their derivatives.

Questions

- What is the equation of the line normal to #f(x)=x^2+8x - 1# at #x=5#?
- What is the equation of the normal line of #f(x)= -2x^3-10x # at #x=2 #?
- What is the equation of the normal line of #f(x)=x^2/(1+4x)# at #x=-1#?
- What is the equation of the normal line of #f(x)=ln(1/x)# at #x=5#?
- What is the slope of the line normal to the tangent line of #f(x) = cos(2x)*sin(2x-pi/12) # at # x= pi/3 #?
- What is the equation of the line normal to # f(x)=-x/(x+4)# at # x=6#?
- What is the equation of the normal line of #f(x)= sinx-cos2x# at #x = pi/8#?
- What is the equation of the line normal to #f(x)=3x^2 -x +1 # at #x=-3#?
- How do you find the equation of the tangent and normal line to the curve #y=x^2+2x+3# at x=1?
- What is the equation of the line normal to #f(x)= x^3/e^x # at #x=2#?
- What is the equation of the line normal to # f(x)=-x/ln(2x^3-x)# at # x=1#?
- What is the slope of the line normal to the tangent line of #f(x) = e^(x-2)+x-2 # at # x= 0 #?
- What is the equation of the line that is normal to #f(x)= ln(x^2-x+1) #at # x= 1 #?
- What is the equation of the normal line of #f(x)=x^3e^-x+x^3# at #x=-5#?
- What is the equation of the line normal to # f(x)=x^2-x-2 # at # x=2#?
- How do you give the equation of the normal line to the graph of #y=2xsqrt(x^2+8)+2# at point (0,2)?
- What is the slope of the line normal to the tangent line of #f(x) = e^(x^2-1)+2x-2 # at # x= 1 #?
- What is the equation of the normal line of #f(x)=sqrt(x/(x+1) # at #x=4 #?
- What is the equation of the line that is normal to #f(x)=-2x^3-3x^2+5x-2# at # x=1 #?
- What is the slope of the line normal to the tangent line of #f(x) = sec^2x-sin^2x # at # x= (pi)/12 #?