I have a function for a university's tuition and I'm supposed to find f'(3) and f('12). Eval and Interpret. Also, I'm supposed to do the same for the second derivative. I just want to make sure my answers look correct and would appreciate any comments. I also need help with understanding the 2nd derivative.
My F(X) = -1.7407x^4+ 60.937x^3 - 586.58x^2 + 2239.3x + 12488
#5) Find the First Derivative, Interpret F'(3), F'(12)
F(X) = -1.7407x^4+ 60.937x^3 - 586.58x^2 + 2239.3x + 12488
F'(X) = -6.9628 x^3+182.811 x^2 -1173.16x + 2239.3
F'(3) = -6.9628 (3)^ 3 +182.811 (3)^2 -1173.16(3) + 2239.3 = $177.12
F'(12) = -6.9628 (12)^ 3 +182.811 (12)^2 -1173.16(12) + 2239.3 = $177.12
Evaluate: The first derivatives X value corresponds to a yearís rate of change. By plugging in X=3, for the third year, into the derivative function, we can see that the University of Pennsylvania studentís tuition in the 3rd year is increasing at a rate of $177.12. At X=13, for the 13th year
6) Find the Second Derivative and F'(X) = -6.9628 x3 +182.811 x2 -1173.16x + 2239.3
-20.8884x2 + 365.622x - 1173.16
-20.8884x2 + 365.622x - 1173.16=0
X=4.230867 and X=13.274538 =0
Evaluate: I don't know what the second derivative is showing me, but was told to solve at y=0 and evaluate.
Thanks in advance!