Find the point (x,y), at which the graph of y=3x2+4x−5 has a horizontal tangent. The slope, m, of a curve y=f(x) at any

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Find The Point X Y At Which The Graph Of Y 3x2 4x 5 Has A Horizontal Tangent The Slope M Of A Curve Y F X At Any 1 (34.77 KiB) Viewed 41 times

Find the point (x,y), at which the graph of y=3x2+4x−5 has a horizontal tangent. The slope, m, of a curve y=f(x) at any point (x,y) is m=h→0lim​hf(x+h)−f(x)​. h→0lim​hf(x+h)−f(x)​=​h→0lim​h3(x+h)2+4(x+h)−5−(3x2+4x−5)​=h→0lim​(6x+3h+4)=6x+4​ So, the slope, m, of the curve at any point (x,y) is m=6x+4. The slope of a horizontal tangent is 0 . Solve for x. 6x+4x​=0=−32​​ The point, (x,y), at which the tangent is horizontal is (−32​,−319​).