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Differentiation: second derivatives, core facts

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This question deals with second derivatives.

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Which of the following are true and which are false?

In the following, $f(x) = \sin(x)$ and $g(t) = \cos(t)$ .

	True	False
From the video, if the second derivative is positive, then the original graph is curving upwards
The second derivative of $f$ is the derivative of the derivative of $f$
The second derivative of $f$ can be denoted by $\frac{d^2f}{dx^2}$
The second derivative of $g$ can be denoted by $\frac{d^2g}{dt^2}$
From the video, if the second derivative is negative, then the original graph is curving downwards
The first derivative of a function is just the derivative of the function

Expected answer:

	True	False
From the video, if the second derivative is positive, then the original graph is curving upwards
The second derivative of $f$ is the derivative of the derivative of $f$
The second derivative of $f$ can be denoted by $\frac{d^2f}{dx^2}$
The second derivative of $g$ can be denoted by $\frac{d^2g}{dt^2}$
From the video, if the second derivative is negative, then the original graph is curving downwards
The first derivative of a function is just the derivative of the function

Score: 0/2

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$f(x) = \simplify{{a1}*x^{n1} + {b1}sin(x)}$ . What is $\frac{d^2 f}{dx^2}$ ?

interpreted as $\displaystyle{}$ Expected answer:interpreted as $\displaystyle{4 + 7 \sin \left ( x \right )}$

$g(t) = \simplify{{a2}ln(t) + {b2} cos(t)}$ . What is $g''(t)$ ?

interpreted as $\displaystyle{}$ Expected answer:interpreted as $\displaystyle{\frac{ 3 }{ t^{ 2 } } - 4 \cos \left ( t \right )}$

Score: 0/2

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Correct answers are not given for the first question, because you should read the information provided to determine what is correct.

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