Barrons AP Calculus - David Bock

Suppose f (1) = 2, f ′(1) = 3, and f ′(2) = 4. Then (f −1) ′(2) (A) equals (B) equals (C) equals (D) equals (E) cannot be deter ...

(A) 0.3 (B) 0.8 (C) 1.5 (D) 1.8 (E) 2 The rate of change of f (x) is least at x (A) −3 (B) −1.3 (C) 0 (D) 0.7 (E) 2.7 Use the f ...

(A) 1 (B) 2 (C) 3 (D) 4 (E) more than 4 The value of f ′(0) obtained using the symmetric difference quotient with f (x) = |x| a ...

On the interval 1 < x < 2, f (x) equals (A) −x − 2 (B) −x − 3 (C) −x − 4 (D) −x + 2 (E) x − 2 Over which of the following ...

(A) (B) −1 (C) 1 (D) (E) 2 Which of the following statements about the graph of f ′(x) is false? (A) It consists of six horizon ...

(B) 1 (C) 2 (D) 3 (E) 4 ...

CHAPTER 4 Applications of Differential Calculus Concepts and Skills In this chapter, we review how to use derivatives to find s ...

Since f ′(x) never equals zero (indeed, it is always positive), f has no critical values. EXAMPLE 3 Find any critical points of ...

B. TANGENTS AND NORMALS Tangent to a curve The equation of the tangent to the curve y = f (x) at point P(x 1 , y 1 ) is y − y 1 ...

substitute this in the equation of the curve, we get Thus y = ±1 and x = ±2. The points, then, are (2, −1) and (−2, 1). EXAMPLE ...

With critical values at x = 0 and x = 3, we analyze the signs of f ′ in three intervals: The derivative changes sign only at x = ...

FIGURE N4–1 Point of inflection A point of inflection is a point where the curve changes its concavity from upward to downward o ...

(a) y ′(c) = 0; y ′′(c) > 0; c yields a local minimum. (b) y ′(c) = 0; y ′′(c) = 0; c yields a local minimum. FIGURE N4–2 (4) ...

FIGURE N4–3 (5) Find all x’s for which y ′′ = 0; these are x-values of possible points of inflection. If c is such an x and the ...

FIGURE N4–4 Verify the graph and information obtained above on your graphing calculator. EXAMPLE 13 Sketch the graph of f (x) = ...

CASE II. FUNCTIONS WHOSE DERIVATIVES MAY NOT EXIST EVERYWHERE. If there are values of x for which a first or second derivative d ...

FIGURE N4–7 Verify the graph on your calculator. F. GLOBAL MAXIMUM OR MINIMUM CASE I. DIFFERENTIABLE FUNCTIONS. If a function f ...

The function has neither a global max nor a global min on any interval that contains zero (see Figure N2–4). However, it does at ...

FIGURE N4–8 Verify the preceding on your calculator, using [−4,4] × [−4, 8]. EXAMPLE 20 Describe any symmetries of the graphs of ...

The region in the first quadrant bounded by the curves of y^2 = x and y = x is rotated about the y- axis to form a solid. Find t ...