Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Test Prep Workbook Update
5th Edition
ISBN: 9780328909148
Author: Prentice Hall
Publisher: Prentice Hall
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In Exercises 5-8, use the definition
ƒ'(a) = lim
x→a
f(x) = f(a)
а
to find the derivative of the given function at the given value of a.
5 f(x) = 1/x, a = 2
6. f(x) x² + 4, a = 1
7. f(x) = √x + 1, a = 3
8. f(x) = = 2x + 3, a = -1
9. Find f(x) if f(x) = 3x - 12.
10. Find dy/dx if y=7x.
X
Use part one of the fundamental theorem of calculus to find the derivative of the function.
g(s) =
(t -
Consider the function
2х + 1
g(x) =
x +1
a) Evaluate the derivative of the function.
b) Sketch the graph of the function, locating the x- and y- intercepts and all
asymptotes.
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- Consider the function f and its derivatives below. f'(x) = -2(2³-32) (³+64)² 6x²(³-128) (3+64)3 f"(x) = f(x) = 3 +64 Fill in the table below. For answers that require intervals, use interval notation and write your answer as a comma-separated list of intervals that are as inclusive as possible. Write "NONE" as your answer, if appropriate. Your answers must be exact or accurate to two decimal places. 2 1.26 38=2 4 1.59 16 2.51 √32 3.17 equations of vertical asymptote(s) of f: equations of horizontal asymptote(s) of f: f is decreasing on: f is increasing on: z-coordinate(s) of each local minimum of f: z-coordinate(s) of each local maximum of f: f is concave down on: f is concave up on: 01 x-coordinate(s) of each inflection point of f: √64=4 128 5.04 Sin den Jaarrow_forwardTo compute the derivative of 2cosx with the chain rule by writing this function as a composition f(g(x)), what is the “outer” function f(x)? Explain your answers clearly.Then compute the derivative of the function.arrow_forwardUse the definition of the derivative of a function to determine f(x) where f(x)=.arrow_forward
- SOLVE STEP BY STEP IN DIGITAL FORMAT FIR W ジッッシ A A * U * ! ! ?? !! ? ?! & i !? X X X 2. Find the derivative of order two of the function h(x)=- 1-² 5-3x 8 & & & X♪ and simplify completely your answer.arrow_forwardSuppose that f:R → R is a function with second derivative f"(x)=x•(x+ 1)³ • (x + 5)ª . Find intervals of concavity-up and concavity-down of f(x), and the x-coordinate(s) of any point(s) of inflection. Explain your answers.arrow_forwardIn Exercises 1-4, use the definition f'(a) = lim la + h) – f(a) h to find the derivative of the given function at the indicated 1. f(x) = 1/x, a = 2 2. f(x) = x? + 4, a = 1 3. f(x) = 3 – x2, a = -1 In Exercises 5-8, use the definition 4. f(x) = x3 + x, a = 0 %3D f(x) – f(a} x - a f'(a) = lim to find the derivative of the given function at the indicated 5. f(x) = 1/x, a = 2 6. f(x) = x2 + 4, a = 1 %3D 7. f(x) = Vx + 1, a = 3 8. f(x) = 2x + 3, a = -1arrow_forward
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- Graph the derivative of the function in Figure (B), omitting points where the derivative is not defined.arrow_forwardFind derivativearrow_forwardThe function f(x) is everywhere continuous and differentiable. Prove that if the function f(x) has two real roots, then its derivative f′(x) has at least one root.arrow_forward
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