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Let f be a differentiable function on \mathbbR such that f(2)=1,\ f'(2)=4. Let \displaystyle \lim_x\to 0\big(f(2+x)\big)^3/x=e^α. Then the number of times the curve y=4x^3-4x^2-4(α-7)x-α meets the x-axis is: | Watch the step-by-step video solution for this NIMCET PYQ.