Consider the function f(x)=-6x + 7x +1. (a) Show that f'(x) > -5 for all r....

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Consider the function f(x)=³-6x² + 7x +1. (a) Show that f'(x) > -5 for all r. Note: You are not allowed to plot the graph of f'(x) and conclude from there, but you should ask yourself what the graph of f' looks like. (b) Show that for every m>-5, there are precisely two points on the graph of f where f'(x) = m. (c) Find an equation of the tangent line to the graph of f at either one of the two points for m = 2. Consider the function f(x)=³-6x² + 7x +1. (a) Show that f'(x) > -5 for all r. Note: You are not allowed to plot the graph of f'(x) and conclude from there, but you should ask yourself what the graph of f' looks like. (b) Show that for every m>-5, there are precisely two points on the graph of f where f'(x) = m. (c) Find an equation of the tangent line to the graph of f at either one of the two points for m = 2.