# How do you sketch the graph #y=sinx+sin^2x# using the first and second derivatives from #0<=x<2pi#?

Please see below.

The graph appears as shown below.

graph{sinx(1+sinx) [-2.917, 7.083, -1.84, 3.16]}

By signing up, you agree to our Terms of Service and Privacy Policy

To sketch the graph ( y = \sin(x) + \sin^2(x) ) using the first and second derivatives:

- Find the first derivative of ( y ) with respect to ( x ) and set it equal to zero to locate critical points.
- Find the second derivative of ( y ) with respect to ( x ) to determine concavity.
- Determine the behavior of ( y ) as ( x ) approaches critical points and at endpoints of the interval ( 0 \leq x < 2\pi ).
- Use the information gathered to sketch the graph within the given interval.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you test #f(x)=8 x^4−9 x^3 +9# for concavity and inflection points?
- Let f'' (x)= 4x^3 - 2x and let f(x) has critical numbers -1, 0, and 1, how do you use the second derivative test to determine which critical numbers, if any give a relative maximum?
- For what values of x is #f(x)=4x^3-3x+5# concave or convex?
- How do you determine whether the function #f(x)= x/ (x^2+2)# is concave up or concave down and its intervals?
- How do you determine the concavity of a quadratic function?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7