Calculus Notes-Questions and Answers Graded A+

Calculus Notes-Questions and Answers Graded A+ tangent line approximation - ANSWER-y=f'(a)(x-a)+f(a) overestimate if f is concave down, underestimate if f is concave up f''(c) is positive - ANSWER-relative max f''(c) is negative - ANSWER-relative min f''(c)=0 - ANSWER-second derivative test fails; use first derivative test f''(x) is positive - ANSWER-concave up f'(x) increases f''(x) is negative - ANSWER-concave down f'(x) decreases directly proportional - ANSWER-(dy/dt)=ky indirectly proportional - ANSWER-(dy/dt)=k/y trapezoidal summation rule concave up - ANSWER-overestimate trapezoidal summation rule concave down - ANSWER-underestimate left Riemann sum f is increasing - ANSWER-underestimate left Riemann sum f is decreasing - ANSWER-overestimate right Riemann sum f is increasing - ANSWER-overestimate right Riemann sum f is decreasing - ANSWER-underestimate RAM (rectangular approximation method) - ANSWER-Riemann sums Mean Value Theorem - ANSWER-If f is continuous and differentiable, then f'(x)=(f(b)-f(a))/(b-a)