Explanation Given information: The graph of y = 3 sin 2 x − cos 2 x at x = 3 π 4 Formula used: 1) d d x [ sin ( f ( x ) ) ] = cos ( f ( x ) ) ⋅ f ′ ( x ) 2) d d x [ cos ( f ( x ) ) ] = − sin ( f ( x ) ) ⋅ f ′ ( x ) 3) Slope of graph m = d y d x = y ′ 4) The equation of the tangent line: y − y 1 = m ( x − x 1 ) , Where, m is slope of line and ( x 1 , y 1 ) Calculation: To find the equation of the line tangent to the graph y = 3 sin 2 x − cos 2 x at x = 3 π 4 first find y , y = 3 sin ( 2 ⋅ 3 π 4 ) − cos ( 2 ⋅ 3 π 4 ) = 3 sin ( 3 π 2 ) + cos ( 3 π 2 ) = 3 ⋅ ( − 1 ) − 0 y = − 3 Therefore, y = − 3 . And Differentiate y = 3 sin 2 x − cos 2 x with respect to x on both sides, y ′ = d y d x = d d x [ 3 sin 2 x − cos 2 x ] = d d x ( 3 sin 2 x ) − d d x ( cos 2 x ) = 3 ⋅ d d x ( sin 2 x ) − d d x ( cos 2 x ) <

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Chapter 8.3, Problem 34E

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To calculate: The equation of the line tangent to the graph of y=3sin2x−cos2x at x=3π4

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Chapter 8.3, Problem 33E

Chapter 8.3, Problem 35E

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Chapter 8 Solutions

EBK CALCULUS & ITS APPLICATIONS

Ch. 8.1 - A right triangle has one angle of /3 radians. What...Ch. 8.1 - Prob. 2CYU Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Give the radian measure of each angle described.Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E

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The equation of the line tangent to the graph of y = 3 sin 2 x − cos 2 x at x = 3 π 4

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Chapter 8 Solutions