Are my book answers wrong?
I've been doing some questions that I thought I was doing right but then I check the book answer and i'm wrong..:
1. Find the slope of the function y=2cosxsin2x at x=pi/2.
So first I differentiated:
y' = (-2sinx)(sin2x) + (2cosx)(cos2x)(2)
= -2sinxsin2x + 4cosxcos2x
Then I determined that sin(pi/2) = 1 and that cos pi/2 = 0 because at 90 degrees, y=1, r=1, x=0.. and sin(pi/2) = y/r = 1/1 = 1.. and cos(pi/2) = x/r = 0/1 = 0 So I subbed these values into my derived equation:
y'(pi/2) = -2(1)(2)(1) + 4(0)(0)(2)
My answer is the slope is -4, however the book answer says 0. Did I go wrong?
2. Find the equation of the line that is tangent to the curve y=2sinx+4cosx at x=pi/4.
So this is what I got when I differentiated y=2cosx+4cosx:
At pi/4: cosx=1/square root of 2, sinx = 1/square root of 2
y'(pi/4) = 2(1/square root of 2) - 4(1/square root of 2)
To get y value:
y(pi/4) = 2(1/square root of 2) + 4(1/square root of 2)
=square root of 2 + square root of 2
y-(square root of 2+ square root of 2)=0(x-(pi/2))
y=square root of 2 + square root of 2
The teacher said the answer is: y=-(square root of 2)x + (square root of 2 / 4) pi + 3(square root of 2)
Where did I go wrong? (Headbang)
3. Find the equation of the line that is tangent to the curve y=2cosx-(1/2)sinx at x=3pi/2.
At 3pi/2: sinx = y/r = 1/1 =1, cosx = x/r = 0/1 = 0
y'(3pi/2) = -2(1) - 1/2(0)
Finding y value:
y(3pi/2) = 2(0) - (1/2)(1)
y-(-1/2)=-2(x - 3pi/2)
y=-2x + 3pi + 1/2
Book answer is: 2x + 1/2 -3pi
Why is their 3pi negative, and there 2x is positive?
4. Find the slope of the line that is tangent to the curve y=2sinxcosx at x=pi/4.
At pi/4: sinx= 1/square root of 2, cosx= 1/square root of 2
y'(pi/4) = -2(1/square root of 2)(1/square root of 2)
Book answer: 0
Where did I go wrong? (Thinking)
5. Find the equation of the line that is tangent to the curve y=2cos^3x at x=pi/3.
At x=pi/3, sinx = (square root of 3) / 2
y'(pi/3) = -6[(square root of 3)/2]^2
I'm not really sure.. how would I work that?
Where you have gone wrong
1. SIN2X=0 WHEN X=PI/2
Originally Posted by kmjt
2. aRE YOU SURE YOU QUOTED THE QUESTION CORRECTLY?
Y=2COSX+4COSX WOULD SIMPLY BE Y=6COSX
3. SIN(3PI/2)=-1 SO Y=1/2 AND Y'=2
4. yOU MUST USE THE PRODUCT RULE WHEN DIFFERENTIATING HERE GIVING Y'=2COS^2X-2SIN^2X ALTERNATIVELY WE CAN SAY Y=SIN2X SO Y'=2COS2X
5. HERE YOU NEED THE CHAIN (FUNCTION OF A FUNCTION)( RULE GIVING Y'=-6COS^2XSINX
Hope this helps