MATH 151 Midterm: MATH 151 TAMU Y2010 2010c Exam 2b Solutions
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Solutions-form b: d. an object is moving according to the equation s(t) = t3 9t2 + 15t + 8. The object is moving in the negative direction when v(t) < 0. Now, v(t) = s (t) = 3t2 18t + 15 = 3(t 5)(t 1). Solve v(t) < 0 yields 1 < t < 5: e. find the slope of the tangent line to the parametric curve x = e 5t, y = t cos t at the point (1, 0). Note rst that t = 0 yields the point (1, 0). Thus the slope of the tangent line is m = dy/dt dx/dt evaluated at t = 0. m = m = dy/dt dx/dt. Find the linear approximation, l(x), of f (x) = x2 + 9 at x = 4. The linear approximation for f (x) at x = 4 is. L(x) = f ( 4) + f ( 4)(x ( 4)). f ( 4) = 25 = 5.
