MAT 295 Lecture 7: Derivatives and Rate of Change

• School: Syracuse University
• Department: Mathematics
• Course: MAT 295
• Professor: All

Document Summary

Mat 295-lecture 7- derivatives and rate of change. Derivative definition: the tangent line to the curve y=f(x) at the point (a,f(a)) is the line through (a, f(a)) with slope. Derivative=slope=m=f "(x ) lim h 0 f (a+h) f (a) m= h. **graph of f(x) formula to find slope, the equation should come out to be. X lim h 0 m= f (a+h) f (a) h. F "(x) is read as the derivative of f(x), which is the slope. Example: find the slope of the tangent line to the curve y=x2 at x=a y=x2 lim h 0 m= Plug in a and a+h into x2 lim h 0 m= f (x2+h) f (x2) h a 2 a+h 2 f f lim h 0 lim h 0 a2+2ah+h2 a2 h lim h 0 h(2a +h) h. The final answer would be the slope of the tangent line at point (a, f(a)) of f(x) is.