What are the points of inflection, if any, of f(x)=5 cos^2 x-10 sin x on x in [0, 2pi]?
Zorgozo58
Answered question
2023-02-15
What are the points of inflection, if any, of on ?
Answer & Explanation
We have: ;
To find the points of inflection, we must calculate the function's second derivative:
The points of inflection are those where the second derivative equals zero:
One of the Pythagorean identities is .
We can rearrange this so that we get:
Let's apply this rearranged identity to get:
Rearrange this to create a quadratic equation:
Thus, let's factorise using the middle-term break:
We now have a product equal to zero, so one of the multiples must also be equal to zero:
or
However, the domain is given as .
Hence, the points of inflection occur at , and .
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