I only need the answers for parts d and e. I don't need a, b, or c. Thank you. Managing fuel costs is always a challenge in the airline industry as the price of jet fuel can be volatile. In orderto analyze fuel needs, a certain company recorded the rate of fuel use by one of their airplanes and the datafrom that flight is shown below. This data resulted in a twice-differentiable function that is always increasing.t (minutes)F(t)(gallons/minute)2030354040505570659070 a. Use data from the table to find an approximation for F'(60). Show how you obtained your answer.Indicate appropriate units.b. Suppose that the rate at which the fuel was being used was increasing fastest 45 minutes into theflight. What is the value of F"(x) at this time? Explain your reasoning.90c. Use a right Riemann sum with 5 intervals to approximate the value of F(t)dt. Is yourapproximation an under-estimate or an over-estimate for the actual value of ["F(t)dt? Explain yourreasoning.90d. Explain the meaning of "F(t)dt for 0sx<90 in the context of this problem.e. Explain the meaning of -F(t)dt for 0

d. Given: Ft is a function representing rate of fuel use (in gallons/minute) and, t represents time…

Managing fuel costs is always a challenge in the airline industry as the price of jet fuel can be volatile. In order to analyze fuel needs, a certain company recorded the rate of fuel use by one of their airplanes and the data from that flight is shown below. This data resulted in a twice-differentiable function that is always increasing. t (minutes) F(t) (gallons/minute) 20 30 35 40 40 50 55 70 65 90 70