For f(x)=4sin(x2) between x=0 and x=3, find the coordinates of all intercepts, critical points, and inflection points to two decimal places. in each part, enter your answers in increasing order of x values. round your answers to two decimals.

Intercepts:

x = 0, y = 0

x = 1.77, y = 0

x = 2.51, y = 0

Critical points:

x = 1.25, y = 4

x = 2.17 , y = -4

x = 2.8, y = 4

Inflection points:

x = 0.81, y = 2.44

x = 1.81, y = -0.54

x = 2.52, y = 0.27

Step-by-step explanation:

We can find the intercept by setting f(x) = 0

where n = 0, 1, 2,3, 4, 5,...

Since we are restricting x between 0 and 3 we can stop at n = 2

So the function f(x) intercepts at y = 0 and x:

x = 0

x = 1.77

x = 2.51

The critical points occur at the first derivative = 0

or

where n = 0, 1, 2, 3

Since we are restricting x between 0 and 3 we can stop at n =  2

So our critical points are at

x = 1.25,

x = 2.17 ,

x = 2.8,

For the inflection point, we can take the 2nd derivative and set it to 0

We can solve this numerically to get the inflection points are at

x = 0.81,

x = 1.81,

x = 2.52,

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step-by-step explanation:

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