how to find the first and second derivative of a graph Differentiation allows us to determine the change at a given point We will use that understanding as well as different theorems such as FTOA IVT EVT MVT Rolle s Theorem first derivative
To find the derivative use the equation f x f x dx f x dx replacing f x dx and f x with your given function Simplify the equation and solve for dx 0 Replace dx in the equation with 0 Explain how the sign of the first derivative affects the shape of a function s graph State the first derivative test for critical points Use concavity and inflection points to explain how the sign of the second derivative affects the shape of a function s graph
how to find the first and second derivative of a graph
how to find the first and second derivative of a graph
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Question Video Finding The Second Derivative Of Trigonometric
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Second Derivative Test YouTube
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If you know that the first derivative of a function is the slope of the original function the second derivative is the slope of the first derivative For instance the first derivative of a distance versus time graph gives you velocity whereas The first derivative of a function gave us a test to find if a critical value corresponded to a relative maximum minimum or neither The second derivative gives us another way to test if a critical point is a local maximum or minimum
The first derivative test provides an analytical tool for finding local extrema but the second derivative can also be used to locate extreme values Using the second derivative can sometimes be a simpler method than using the first derivative A derivative is often shown with a little tick mark f x The second derivative is shown with two tick marks like this f x Example f x x 3 The derivative of x 3 is 3x 2 so f x 3x 2 The derivative of 3x 2 is 6x so f x 6x A derivative can also be shown as dy dx and the second derivative shown as d2y dx2
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Find f x for f x 3x 7 First we need to find the first derivative f x 21x 6 nonumber Then we take the derivative of that function f x frac d dx left f x right frac d dx left 21x 6 right 126x 5 nonumber In this section we will discuss what the second derivative of a function can tell us about the graph of a function The second derivative will allow us to determine where the graph of a function is concave up and concave down The second derivative will also allow us to identify any inflection points i e where concavity changes that a
If the original graph is of a parabola rather than a circle then the graph of the derivative is a straight line since d dx ax bx c 2ax b If the original graph is a circle then the graph of the derivative will be similar but opposite to the purple math image you linked to How do you find local maximum value of f using the first and second derivative tests f x x sqrt 9 x How do you find and classify all the critical points and then use the second derivative to check your results given y x 2 10x 11
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how to find the first and second derivative of a graph - A derivative is often shown with a little tick mark f x The second derivative is shown with two tick marks like this f x Example f x x 3 The derivative of x 3 is 3x 2 so f x 3x 2 The derivative of 3x 2 is 6x so f x 6x A derivative can also be shown as dy dx and the second derivative shown as d2y dx2