Question

Find an equation of a line tangent to y = 2sin x whose slope is a maximum value in the interval (0, 2π]

Answer 1

take second derivative, find critical numbers, do the test to see which number result in the maxima. Plug that number in your first derivative (in the x) to find that number, and this will be your slope. Plug that number in again in the original equation to find your y coordinate. Use the point-slope formula to rearrange everything into y = mx + b

Answer 2

hope this helps, if my steps are confusing then find the first and second deriv first and ask me the next step (but the above is how you would get your answer)

Answer 3

would the second derivative be f''(x)=-2sinx? and the critical number is 0.
Then f'(x)=2cosx and f'(0)=2 so the slope is m=2?
Then f(x)=2sinx and f(2)=1.82 (the y-coordinate)
what would the x value be?

y-1.82=2(x-?)

Answer 4

If i were to find the first derivative which is 2cosx and set it to zero to find the critical numbers i would get x=pi/2, 3pi/2. Then make the chart where i would sub in each of these values (0, pi/2, 3pi/2, and 2pi) into the original f(x) and find the maximum value which is the slope. would that be correct?

Answer 5

slope = 2 is right
f(2) = 1.82 looks right
the "?" in your equation should also be 2. And I think that it's good to go!

Note: don't have a calculator with me at the moment, so I just guess-timate your answers. If you plug in the calculator right then the answer should be correct

Answer 6

oh, ok thanks i will try that!

Answer 7

and yup, your second question is correct

Answer 8

so i can do either one?

Answer 9

also, why is x=2?

Answer 10

x=2 where?

Answer 11

i was wondering why the x value is 2

Answer 12

oh, so first when you find the critical numbers in the second derivative, you find that they are 0 and 2pi right? ) will give you the maxima, so when you plug in 0 to the first derivative you get 2, so that's why x = 2