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If $f(x)=a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x^{1}+a_{0} .$ Find the first five derivatives of $f$ What happens for the sixth and higher order derivatives?

$4 a_{4} x^{3}+3 a_{3} x^{2}+2 a_{2} x+a_{1} ; 12 a_{4} x^{2}+6 a_{3} x+2 a_{2} ; 24 a_{4} x+6 a_{3} ; 24 a_{4} ; 0$ they are all 0

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 3

Concavity and the Second Derivative

Derivatives

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04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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questions. Seven states that if F of X equals a four x to the fourth plus a three x to the third, plus a two x squared plus a one x two the first plus a not they would like you to find the first five derivatives and then what happens? Uh, for the six and higher order derivatives, So finding those first five f prime of X is equal to four a four x to the third plus three 83 X squared plus two a two X plus eight one after all, primer backs is that an equal to 12? A. Four x squared plus six a three x plus two a two The third derivative of F A bex is then equal to 24 a four x plus six. A three fourth derivative of F of X is that in just 24 a four and fit derivative, it is just equal to zero. So from there you can tell that the six derivative and higher he's just going to be equal to zero. And those are all your answers for Question seven

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