calculus
for what value(s) of x does the slope of the curve y=-x^3+3x^2+1 take on its largest value
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The slope of the curve y=-x^3+3x^2+1 is equal to -3x^2+6x. To find the maximum value of the slope, we need to solve for the derivative, which is equal to 6x-6. The largest value for the slope occurs when x=1, since setting the derivative to zero results in a critical point at x=1. Therefore, the slope of the curve y=-x^3+3x^2+1 is largest at x=1.
