[1.7] Coaxing the Derivative out of NOTHING! First we start with ( )yf xand what we know about AROC at xaslope of the secant from (,()) to (,())=()( )AROC of xaa f aah f ahf ahf ayfhxNowAs hgets smaller and smaller and smaller the length of the secant line gets ever smaller, but at the same time the slope of the secant line gets ever closer to the slope of the tangent line. Even though we don’t really know the value of the slope of the tangent line we know the secant line slope is getting closer to it. For small the slope of the secant from ()( )Slope of the tangent to at the input xhf ahf afhNow for zee Magic…Vee do zee CALCULUS undThe secant line disappears, thus ceases to exist and therefore has no slope at the same “moment” that its slope becomes the slope of the tangent line. We say the AROC is no longer
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