The derivative, f'(x) = 6x^2+1, is never negative, so f(x) is monotonic, hence invertible.
f'(-2) = 6(-2)²+1 = 25
If point (-2, -26) is on the graph of function f(x), and the slope is 25 there, then (-26, -2) is on the graph of f⁻¹(x), and the slope is 1/25 there. The equation of the tangent line throught that point can be written in point-slope form as
... y +2 = (1/25)(x +26)
Let Y denote the maximum age of rabbit.
To calculate probability for Y=a from given table, we need to divide frequency corresponding to y=a with sum of frequencies.
For example P(Y=0) =
Like that P(y=1) = 0.1563, P(Y=2) = 0.2891, P(y=3) = 0.2615, P(Y=4) = 0.1516,
P(Y=5) = 0.0667, P(Y=6) = 0.0391,P(Y=7) = 0.0067, P(Y=8)=0.004 and P(Y=9) =0.
a) P(Y>5) = P(Y=6)+P(Y=7)+P(Y=8)+P(Y=9)
= 0.0391+0.0067+0.004+0 = 0.0498
b) P(2<Y<6) = 0.2615+0.1516+0.0667 = 0.4798
c) P(Y≥3) = 0.2615+0.1516+0.0667+0.0391+0.0067+0.004+0= 0.5296
d)P(Y<6) = 0.02493+0.1563+0.2891+0.2615+0.1516+0.0667 =0.95013
e)If we add (a) and (d), we will get 0.0498+0.95013 = 0.99993≈1
Not surprised,since this is nothing but addition of probabilities for all Y values.
That's we got 1 since numerator and denominator are same.