PHYSICS 2 Lecture 8: PHYSICS 2 - Lecture 8 - Differentiation, Slopes, Maxima and Minima
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Physics 2 - lecture 8 - differentiation, slopes, maxima and minima. = 1 w (log base e) log(w) dw d a = a a 1 n l = l x x dx og e. Chain rule with t as df dx dx dt. If f is changing with x as df/dx and x is changing with t as dx/dt, then f is changing. This chain rule can be extended to include more links such as df dx dx dt dy dt. Find the derivative of f=cos(x +wx) with respect to x. Then f=cos(u) du = s df dx = df du dx. Red line is tangent at x=-3. 5, f(-3. 5)=-14. Its equation is y-(-15)=m (x-(-3. 5)) with m (slope) given by the derivative df/dx evaluated at x=-3. 5. Curvature tells us how the slope is changing. If slope is increasing with x, then curvature is positive as in the region to the right of the green tangent.
