1.) Find the slope of a line tangent to the curve of the function y=(2x+1)(x^4-1

Question

1.) Find the slope of a line tangent to the curve of the function y=(2x+1)(x^4-1) at the point (0,1). Do not multiply the factors before taking the derivative. Use the derivative evaluation feature of a graphing calculator to check your results. Find the derivative of the function. Choos the correct answer below. a. dy/dx=(2) (4x^3)+(x^4 -1)(2x + 1) b. dy/dx=(2x +2) (4x^3) + (x^4 - 1) (1) c. dy/dx=(2x + 1) (x^3)+(4x^4 - 1)(2) d. dy/dx=(2x + 1) (4x^3) + (x^4 -1) (2) 2.) A computer using data from a refrigeration plant, estimated than in the event of a power failure to the temp C (in?) in the freezers would be given by C = 4t/(0.03t+3) - 10, where t is the number of hours after the power failure. Find the time of change of temperature after 7.0h What is the time rate of change after 7.0 h in ?/h ? (Round to one decimal as needed)

Explanation / Answer

1.) d is correct. slope value is obtained by putting (0,1) = -2 2.) it can be obtained by differentiating the C with respect to t C' = 12/(0.03t+3)^2 putting t= 7 we get C' = 1.16 or 1.2(upto 1 decimal)

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