Barrons AP Calculus

103. 1. 2. 3. (D) The average rate of change is represented by the slope of secant segment . There appear to b ...

(B) Since y′ = e−x(1 − x) and e−x > 0 for all x, y′ = 0 when x = 1. (D) Th ...

(B) We want to approximate the change in area of the square when a side of length ...

(B) The graph must be concave upward but decreasing. (B) The object moves to the ...

(D) See the figure, which shows the motion of the particle during the time interval −2 ...

. (C) Since . ; when . (B) See Figure N4−22. Replace the printed measurements of the radius and h ...

y − 2 = m(x − 1) with intercepts as indicated in the figure. The area A of the triangle ...

q′ = 0 if x = 3. Since q′ is negative to the left of x = 3 and positive to ...

(D) Since ab > 0, a and b have the same sign; therefore f ′′(x) = 12ax^ ...

(E) The slope ; at the given point and y = 1. The equation is ...

(A) Acceleration is the derivative of velocity. Since the velocity is linear, its derivati ...

(D) The graph of f ′(x) = x sin x − cos x is drawn here in the window [0,4] × [−3,3] ...

(C) The direction of a is . Since and , the acceleration is always directe ...

(D) At x = a, f ′ changes from increasing (f ′′ > 0) to decreasing (f ′′ < 0). Thus ...

(B) Maximum acceleration occurs when the derivative (slope) of velocity is greatest. (B) ...

91. 92. 1. 2. 3. 4. 5. (C) Since f ′(6) = 4, the equation of the tangent at (6, 30) is y − 30 = 4(x − 6). The ...

(B) Rewrite: . Using (3) yields . (A) This is equivalent to . (E) Rewrite as (2t^2 ...

(C) Use (17); rewrite as . (B) Rewrite as . Use (3). Compare the integrands in Questions ...

(E) Rewrite as and use formula (3). (B) The integral is equal to sin 2θ dθ. ...

Use formula (3). (B) The integral is equivalent to . Use formula (12). (E) Use formula ( ...