Explanation Formula used: d d x ( x ) = 1 2 x (1) Calculation: Given curve is y = 6 x − 2 . Given point is x = 3 . Use the above formula to differentiate the function with respect to x . y ′ ( x ) = d d x ( 6 x − 2 ) = 1 2 6 x − 2 d d x ( 6 x − 2 ) = 1 2 6 x − 2 ( 6 ) = 3 6 x − 2 First derivative of the function is known as slope. That is, slope: y ′ ( x ) = 3 6 x − 2 . Substitute x = 3 in y ′ ( x ) . y ′ ( 3 ) = 3 6 ( 3 ) − 2 = 3 18 − 2 = 3 16 = 3 4 Thus, slope: m = 3 4

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 4, Problem 57RE

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To find: The slope of the tangent line to the curve y=6x−2 at x=3 and the equation of the tangent line.

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Chapter 4, Problem 56RE

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A graph of the function f is given below: Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1 Of is defined at a. If is not defined at x = a. Of is continuous at x = a. If is discontinuous at x = a. Of is smooth at x = a. Of is not smooth at = a. If has a horizontal tangent line at = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. If has no tangent line at x = a. f(a + h) - f(a) lim is finite. h→0 h f(a + h) - f(a) lim h->0+ and lim h h->0- f(a + h) - f(a) h are infinite. lim does not exist. h→0 f(a+h) - f(a) h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

The graph below is the function f(z) 4 3 -2 -1 -1 1 2 3 -3 Consider the function f whose graph is given above. (A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter "DNE". If a limit can be represented by -∞o or ∞o, then do so. lim f(z) +3 lim f(z) 1-1 lim f(z) f(1) = 2 = -4 = undefined lim f(z) 1 2-1 lim f(z): 2-1+ lim f(x) 2+1 -00 = -2 = DNE f(-1) = -2 lim f(z) = -2 1-4 lim f(z) 2-4° 00 f'(0) f'(2) = = (B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left- continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If there are none, enter "none". Discontinuous at z = Left-continuous at x = Invalid use of a comma.syntax incomplete. Right-continuous at z = Invalid use of a comma.syntax incomplete. (C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5).…

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Chapter 4 Solutions

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

Ch. 4.1 - YOUR TURN 1 find f′(t). Ch. 4.1 - YOUR TURN 2 find dy/dx. Ch. 4.1 - Prob. 3YT Ch. 4.1 - Prob. 4YT Ch. 4.1 - Prob. 5YT Ch. 4.1 - Prob. 1WE Ch. 4.1 - Prob. 2WE Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...

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The slope of the tangent line to the curve y = 6 x − 2 at x = 3 and the equation of the tangent line.

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Chapter 4 Solutions