Section 1.4 We only know one point on the tangent line; therefore, determining the slope of...

  

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Section 1.4 We only know one point on the tangent line; therefore, determining the slope of the tangent line is not as straight- forward as determining the slope of the secant line (of which we know two points). Determining the slope of the tangent line to f(x) = x² at the point P(1,1). What do we need? ● Choose another point Q and determine the Keep changing the ● ● Q (x,x²) (1.5.. h m= y₂-y/₁ h to get closer to P msec What do we need? ● Choose another point Q and determine the Keep changing the ● ● Q (x,x²) (1.5,) (1.1,. (1.01,. (1,______) (0.99, (0.9,_ (0.5,. h Difference Quotient: m= to get closer to P Уz-yi h msec The slope of the tangent line is the limit of the slopes of the secant lines. The goal is to get h closer to 0. f(x+h)-f(x) h Section 1.4 We only know one point on the tangent line; therefore, determining the slope of the tangent line is not as straight- forward as determining the slope of the secant line (of which we know two points). Determining the slope of the tangent line to f(x) = x² at the point P(1,1). What do we need? ● Choose another point Q and determine the Keep changing the ● ● Q (x,x²) (1.5.. h m= y₂-y/₁ h to get closer to P msec What do we need? ● Choose another point Q and determine the Keep changing the ● ● Q (x,x²) (1.5,) (1.1,. (1.01,. (1,______) (0.99, (0.9,_ (0.5,. h Difference Quotient: m= to get closer to P Уz-yi h msec The slope of the tangent line is the limit of the slopes of the secant lines. The goal is to get h closer to 0. f(x+h)-f(x) h

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Solution Qxx h xx 15 225 h 151 65 P1 1 x y yy h m 2251 05 1... View the full answer