The atmospheric pressure of the air changes with height above sea level. The pressure of the air at a given height above sea level can be measured by the differentiable function f(h), in psi, where h is measured in meters. What are the units of f^('')(h)? meters psi meters / psi psi / meter meters //psi^(2) psi // meter ^(2)

Question

The atmospheric pressure of the air changes with height above sea level. The pressure of the air at a given height above sea level can be measured by the differentiable function  f(h), in psi, where  h is measured in meters. What are the units of  f^('')(h)? meters psi meters / psi psi / meter meters  //psi^(2) psi  // meter  ^(2)

Bytelearn · Accepted Answer

Understand Second Derivative Meaning: Understand the meaning of the second derivative in terms of units. The second derivative f''(h) represents the rate of change of the rate of change of atmospheric pressure with respect to height. Since f(h) is given in psi and h is given in meters, the first derivative f'(h) would have units that describe the rate of change of pressure with respect to height.Determine First Derivative Units: Determine the units of the first derivative f'(h). The first derivative f'(h) would have units of psi per meter (psi/m), because it represents the change in pressure (in psi) for a change in height (in meters).Determine Second Derivative Units: Determine the units of the second derivative f''(h). The second derivative f''(h) would have units of the first derivative's units per meter. Since the first derivative has units of psi/m, the second derivative would have units of (psi/m) per meter, which simplifies to psi per meter squared (psi/m^2).

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