# calculus

find all extrema in the interval [0, 2pi] if y=sinx + cosx

and also

a certain item sells for \$30. if the cost of producing this item is given by C=.05^3 + 100, find the mariginal profit when x=10.

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. To find the extrema, do the First Derivative Test.

y = sinx + cos x
y'= cosx - sinx
The extrema always occur when the derivative is zero, so set it equal to zero.

y' = cosx - sinx = 0
= cosx = sinx
cosx/cosx = sinx/cosx
1 = tanx
x = pi/4, 5pi/4

Make a sign chart...
y' increases on (0, pi/4) and (5pi/4, 2pi)
y' decreases on (pi/4, 5pi/4)
A max occurs at pi/4, a min occurs at 5pi/4.

The extrema are...
Relative maximum = √2 @ x = pi/4
Relative minimum = -√2 @ x = 5pi/4

I think you've made a mistake on your second problem. There is no variable in the C function.

1. 👍
2. 👎
3. ℹ️
4. 🚩
2. C=.05x^3+100

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### trigonometry

how do i simplify (secx - cosx) / sinx? i tried splitting the numerator up so that i had (secx / sinx) - (cosx / sinx) and then i changed sec x to 1/ cosx so that i had ((1/cosx)/ sinx) - (cos x / sinx) after that i get stuck

Which of the following are trigonometric identities? (Can be more then one answer) tanx cosx cscx = 1 secx-cosx/secs=sin^2x 1-tanxtany=cos(x+y)/cosxcosy 4cosx sinx = 2cosx + 1 - 2sinx Find all solutions to the equation cosx

3. ### Trigonometry

4. Find the exact value for sin(x+y) if sinx=-4/5 and cos y = 15/17. Angles x and y are in the fourth quadrant. 5. Find the exact value for cos 165degrees using the half-angle identity. 1. Solve: 2 cos^2x - 3 cosx + 1 = 0 for 0

4. ### trig

Find all solutions of the equation 2sin^2x-cosx=1 in the interval [0,2pi) x1= ? x2=? x3=?

1. ### Calculus

determine the absolute extreme values of the function f(x)=sinx-cosx+6 on the interval 0

2. ### Maths

Find the general solution of equation sinx + cosx = 2 (root2) (sinx)(cosx)

3. ### Calculus

Find all points of extrema on the interval [0, 2pi] if y=x+sinx (-1.-1+(3pi/2)) (pi, pi) (-1,0) ((3pi/2), 0) none of these I got pi as my critical number but I'm confused with the intervals.

4. ### Trig.......

I need to prove that the following is true. Thanks (2tanx /1-tan^x)+(1/2cos^2x-1)= (cosx+sinx)/(cosx - sinx) and thanks ........... check your typing. I tried 30º, the two sides are not equal, they differ by 1 oh , thank you Mr

1. ### Pre-Calc : Verify the Identity

Verify the Identity: sin(x+π)/cos(x+3π/2) =tan^2x-sec^2x I've done: sinxcosπ+cosxsinπ / cosxcos(3π/2) - sinxsin(3π/2) sinx(-1) + cosx(0) / cosx(0)- sinx(-1) -sinx/sinx What do I do from here? Or what did I do wrong?

2. ### Calculus

1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2]. 2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[-4,-2]. If Rolle's Theorem can be

3. ### Math

(sinx - cosx)(sinx + cosx) = 2sin^2x -1 I need some tips on trigonometric identities. Why shouldn't I just turn (sinx + cosx) into 1 and would it still have the same identity?

4. ### Calculus

Find the relative extrema of the function f(x) = 1/2 x - sinx on the interval (0, 2 pie) please show me how you got this!!