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jahjah1158
21.11.2019 •
Mathematics
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.
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Ответ:
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
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
Since we are restricting x between 0 and 3 we can stop at n = 2
So our critical points are at
x = 1.25,![y = f(1.25) = 4sin(1.25^2) = 4](/tpl/images/0384/3632/65eac.png)
x = 2.17 ,![y = f(2.17) = 4sin(2.17^2) = -4](/tpl/images/0384/3632/a822c.png)
x = 2.8,![y = f(2.8) = 4sin(2.8^2) = 4](/tpl/images/0384/3632/b0126.png)
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,![y = f(0.81) = 4sin(0.81^2) = 2.44](/tpl/images/0384/3632/f65fe.png)
x = 1.81,![y = f(1.81) = 4sin(1.81^2) = -0.54](/tpl/images/0384/3632/5bdfc.png)
x = 2.52,![y = f(2.52) = 4sin(2.52^2) = 0.27](/tpl/images/0384/3632/ddc7d.png)
Ответ:
what’s the question?
Step-by-step explanation: