Answer
(a) Show explanation
(b) c = 2
Work Step by Step
(a) We can see in the graph that f(x) is zero at three distinct values of x and hence it is not one-to-one and non-invertible.
(b)Let's calculate the slope of the function to find the largest interval in which it doesn't change sign.
$f'(x)=6x^2+6x-36=6(x^2+x-6) = 6(x^2+3x-2x-36)=6(x+3)(x-2)$ which changes sign from +ve to -ve at $x=-3$ and back to +ve at $x=2$
.
In the interval [-3, 2], our graph is strictly decreasing(and hence one-to-one and consequently invertible) so (-2, 2) is the greatest interval of the form (-c, c) such that f(x) is invertible.
