D Problem #1 Critical numbers Endpoints Plug in critical numbers and endpoints into f(x) to find the largest f(x) Mathboat.com.

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Presentation transcript:

D Problem #1 Critical numbers Endpoints Plug in critical numbers and endpoints into f(x) to find the largest f(x) Mathboat.com

Problem #2 A Mathboat.com

At x=2, f’(x) is decreasing. [f’(x)]’ = f’’(x) f’’ (2) < f’ (2) < f (2) negative zerofour, positive Given: f (2) = 4 From the graph: f’(2) = 0 f’’(2) is negative. Solution: y=f’(x) Problem # C Mathboat.com

Problem #4 C Mathboat.com

Solution: Problem #5 C Mathboat.com

Problem #6 B Mathboat.com

Problem #7 C Mathboat.com

By the definition of inverse: Problem #8 C Set f(x)= -1 Let’s find f’(3) Mathboat.com

Local maximum is the absolute maximum since function is first increasing, then decreasing max Problem #9 D Mathboat.com

B Problem #10 Mathboat.com

Problem #11 A Mathboat.com

Problem #12 B Mathboat.com

Find the points of intersections of these two curves: 2y=x 2 +4 ; y= x 2 Substitute into the formula Problem #13 D Mathboat.com

Problem #14 D By definition of derivative, Mathboat.com

Problem #15 D Mathboat.com

OR By 2 nd fundamental theorem Problem #16 B Mathboat.com

Problem #17 x y dcba - + D Mathboat.com

Problem #18 A Mathboat.com

Factor out Problem #19 C Implicitly differentiate Plug in x=0, y=1 Mathboat.com

Problem #20 E Mathboat.com

Problem #21 D Mathboat.com

Problem #22 B Mathboat.com

Problem #23 D Mathboat.com

y 1.All dashes on the same vertical axis are  does not have y Problem #24 B Mathboat.com

Problem #25 D Mathboat.com

Find critical numbers by finding zero(s) of when is increasing atand Problem #26 C Mathboat.com

Problem #27 C Mathboat.com

Problem #28 B Mathboat.com

Problem #29 B Mathboat.com

Area under the curve = area of the triangle 1 1 By 2 nd Fundamental Theorem of Calculus Problem #30 B Mathboat.com

Find the x-intercepts: Problem #31 C Mathboat.com

Problem #32 A Mathboat.com

= 8 Problem #33 C Mathboat.com

Problem #34 B Mathboat.com

Problem #35 D Mathboat.com

Problem # 36 D Mathboat.com

Problem #37 D Mathboat.com

Problem #38 A By 2 nd Fundamental Theorem of Calculus: Mathboat.com

Problem #39 Graph it! C Mathboat.com

R r Problem #40 E Mathboat.com

Problem #41 B Mathboat.com

Problem #42 _ + D Mathboat.com

Problem #43 B Mathboat.com

3-9 Problem #44 C Mathboat.com

or Problem #45 D Mathboat.com