Calculus 1 : How to find concave down intervals by graphing functions
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Example Questions
Example Question #81 : Intervals
Is the function b(t) concave up, concave down, or neither when t is equal to -3?
Concave up, because
Concave down, because
Concave down, because
Concave up, because
Concave down, because
Is the function b(t) concave up, concave down, or neither when t is equal to -3?
To test for concavity, we need to find the sign of the function's second derivative at the given time.
Begin by recalling that the derivative of a polynomial is found by multiplying each term by its exponent, then decreasing the exponent by 1.
Doing this gets us the following:
Almost there, but we need b"(-3)
b"(-3) is negative, therefore our function is concave down when t=-3
Example Question #1641 : Functions
Determine the intervals on which the function is concave down:
The function is never concave down
The function is never concave down
To determine the intervals on which the function is concave down, we must find the intervals on which the second derivative is negative.
First, we must find the second derivative of the function:
The derivatives were found using the following rules:
Note that for the first rule, the chain rule, as it applies to the natural log, regardless of the constant in front of x, the derivative of the natural log will always be the same.
Next, we must find the values at which the second derivative is equal to zero. This never occurs, so there is no place at which the second derivative is equal to zero. Furthermore, the second derivative is always positive, so the function is never concave down.
Example Question #83 : Intervals
When is the fucntion 
nowhere
To find concavity, you need to find the second derivative. In order to find that, you must first determine the first derivative. When taking the derivative, multiply the exponent by the coefficent in front of the x and then subtract one from the exponent. The first derivative is 
Example Question #2671 : Calculus
Determine the intervals on which the function is concave down:
To determine the intervals on which the function is concave down, we must determine the intervals on which the second derivative of the function is negative.
To start, we must find the second derivative:
The derivatives were found using the following rules:
Next, we must find the values at which the second derivative is equal to zero:
Using these values, we can make our intervals on which we check the sign of the second derivative:
Next, plug in any point on each interval into the second derivative function and check the sign. On the first interval, the second derivative is negative, on the second, it is positive, and on the third, it is negative. The intervals on which the second derivative is negative are concave down:
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