Find {eq}f {/eq} given that {eq}f''(x) = 4 + 6x + 24x^2, \ f(0) = 3, {/eq} and {eq}f(1) = 10 {/eq}.

Question:

Find {eq}f {/eq} given that {eq}f''(x) = 4 + 6x + 24x^2, \ f(0) = 3, {/eq} and {eq}f(1) = 10 {/eq}.

Second Order Derivative:

If the function {eq}y = f\left( x \right) {/eq} has a derivative at each point {eq}x {/eq} in its domain of definition, then its derivative {eq}f'\left( x \right) {/eq} form a function of {eq}x {/eq}. The function {eq}Y = f'\left( x \right) {/eq} may have a derivative, which is called the second order derivative of the function {eq}y = f\left( x \right) {/eq}, and denoted as {eq}y = f''\left( x \right) {/eq}

Answer and Explanation: 1

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Given

The second order derivative of the function is given as {eq}f''\left( x \right) = 4 + 6x + 24{x^2} {/eq} and {eq}f\left( 0 \right) = 3,f\left(...

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Calculating Higher Order Derivatives

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Chapter 8 / Lesson 10
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Higher order derivatives, 2nd, 3rd, and 4th order derivatives, can be calculated using the change in rate of acceleration, known as 'jerk'. Learn how to find these higher order derivatives and the concept of 'jerk' in mathematics.


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