The force exerted by a special compression device is given as function of compression x as F x ( x ) = kx ( x − ℓ ) for 0 ≤ x ≤ ℓ , where ℓ is the maximum possible compression and k is a constant. T

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The force exerted by a special compression device is given as function of compression x as F x ​ ( x ) = kx ( x − ℓ ) for 0 ≤ x ≤ ℓ , where ℓ is the maximum possible compression and k is a constant. The magnitude of the force exerted by the device under compression is maximum when compression is :

TestHub · Accepted Answer

F ( x ) = k x ( x − ℓ ) = k ( x 2 − ℓ x ) . For maximum force, d x d F ​ = k ( 2 x − ℓ ) = 0 ⇒ x = 2 ℓ ​ (second derivative 2 k > 0 gives the extreme of magnitude, the force being negative there, so the magnitude of the force is maximum at ℓ /2 ).

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