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Social Sciencef(x)-f(a)a. Use the definition mtan= limto find the slope of the line tangent to the graph of f at Pх-аXab. Determine an equation of the tangent line at P.c. Plot the graph of f and the tangent line at Pf(x)=x2-7, P(-3,2)
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f(x)-f(a) a. Use the definition mtan = lim to find the slope of the line tangent to the graph of f at P х-а Xa b. Determine an equation of the tangent line at P. c. Plot the graph of f and the tangent line at P f(x)=x2-7, P(-3,2)
Expert Answer
Part (a) P(-3, 2) = [a, f(a)]
Hence, a = -3, f(a) = 2
Please see the whiteboard for the calculation of mtan = slope of the tangent line = -6
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Га) — 2 x2- 7-2 lim x--3 lim 1—-3х — (—3) mtan 2-9 lim x 3 3 lim (x -3) =-3 - 3 -6
Part(b)
Equation of the tangent line at P will be:
[y - f(a)] = mtan[x - (-3)]
Hence,...
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