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Solve the given problems by finding the appropriate derivatives.The deflection $y$ (in $\mathrm{m}$ ) of a $5.00-\mathrm{m}$ beam as a function of the distance $x$ (in $m$ ) from one end is $y=0.0001\left(x^{5}-25 x^{2}\right)$. Find the value of $d^{2} y / d x^{2}$ (the rate of change at which the slope of the beam changes) where $x=3.00 \mathrm{m}.$

Calculus 1 / AB

Chapter 23

The Derivative

Section 9

Higher Derivatives

Derivatives

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in this problem, we need to find the value of v two, I. D X two when X is equal to three. Now, the value of why is given to be equal to 0.1 times X to the power five minus 25 X square. But let's first find the first derivative. So that will be dy dx is equal to 0.1 times the derivative of actually power five, which is five times actually power four minus 25 times the derivative of X square which is two X. So this will be equal to 0.1 times five X. To the power four minus 50 X. Next let us determine the second derivative. That will be the derivative of this expression over here. So that will be equal to 0.1 times five times the derivative of X. To the power for which is four times X to the power four minus one. So that's xq minus 50 times the derivative of X, which is one. So this will be 0.1 times 20 X cubed minus 50. Now we need to find the value of the second derivative at the point X is equal to three, so we substitute X equals to three, so we have 0.1 times 20 times three Q minus 50 and the value of this is equal to 0.49 and the answer is 0.49

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