# The annual profit of the Digitronics company x yrs from now is predicted to be P(x)=5.27x^0.3 - 0.463x^1.52 million dollars for (0`<=x` `<=8` ). Evaluate the profit function and its first and...

The annual profit of the Digitronics company x yrs from now is predicted to be P(x)=5.27x^0.3 - 0.463x^1.52 million dollars for (0`<=x` `<=8` ). Evaluate the profit function and its first and second derivatives at x=3 and interpret the answer.

justaguide | College Teacher | (Level 2) Distinguished Educator

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The annual profit of the Digitronics company after x years is predicted to be P(x)=5.27x^0.3 - 0.463x^1.52 million dollars for `0<= x<=8` .

The first derivative of the profit function is:

P'(x) = 1.581*x^(-0.7) - 0.70376*x^0.52

The second derivative of the profit function is:

P''(x) = -1.1067*x^-1.7 - 0.3659552*x^-0.48

At x = 3,

P(3) = 4.8680861020080144.868086102008014

P'(3) = -.5132924188589684

P''(3) = -.3869496236565245

P(3) gives the profit at x = 3, P'(3) gives the rate at which the profit is changing at x = 3 and P''(3) gives the rate at which the change in profit is changing at x = 3.