Slope of Tangent and Normal
Two related slopes
At a point on a curve y=f(x), the derivative f′(x) gives the slope of the tangent line, the line that just touches the curve there. The normalis perpendicular to the tangent at that same point, so its slope is the tangent slope's negative reciprocal:
mnormal=−mtangent1Worked example
Find the slope of the normal to the curve y=2x2−3sinx at x=0.
Solution: The tangent slope is the derivative:
y′=4x−3cosxAt x=0: y′(0)=0−3(1)=−3. The normal slope is the negative reciprocal:
mnormal=−−31=31Continue learning
Finding a tangent line's equation, not just its slope, is the natural next step.