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How can you know that a value is the minimum of a function?
When the first derivative of the function is equal to zero and the second derivative is positive.
What are the uses of derivatives?
A derivative of a function represents that equation's slope at any given point on its graph.
How do you find points of inflection in calculus?
Points of inflection on curves are where the curvature changes sign, such as when the second deriviative changes sign
Why the derivative is set equal to zero?
The first derivative is set to zero to find the critical points of the function. A critical point can be a minimum, maximum, or a saddle point. There's a reason for this. Suppose a differentiable function f:R->R has a maximum at x=a. Then the function goes down to the right of a, which means f'(a)
What is the derivative of ln cos x?
The derivative of the natural log is 1/x, therefore the derivative is 1/cos(x). However, since the value of cos(x) is submitted within the natural log we must use the chain rule. Then, we multiply 1/cos(x) by the derivative of cos(x). We get the answer: -sin(x)/cos(x) which can be simplified into -tan(x).
