MATH 31A Midterm: Math 31A Exam 12
Document Summary
If we cannot get an exact value, derivatives/tangent lines can help us to get a good estimate. Slopes measure rate of change (secant lines give av- erage rate of change, tangent lines give instanta- neous rate of change). Example: find the average rate of change to the curve y = x2 from x = a to x = b. Example: find the instantaneous rate of change to the curve y = x2 at x = (a + b)/2. (see also pm1. 6, m1. 5) Finding tangent lines is important since we can use it to get information about the function. Example: find the tangent line to y = sin( x2) x at x = 1. Example: for f (x) = 2x3 12x2 + 7x + 2 the y-intercept is 2. Find the (unique) x 6= 0 so that the y-intercept of the tangent line is also 2. (see also pm1. 3, pm1. 5, m1. 1, m1. 4, pfb. 4, pfc. 4)
