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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
Posted: Thu Jul 14, 2022 4:35 pm
by answerhappygod
- 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 42 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→0limhf(x+h)−f(x). h→0limhf(x+h)−f(x)=h→0limh3(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).