Let f(x)=7x-x^(2).
(a) Find the slope of the tangent line to the graph of f at the point (1,6) using the definition given below.
f^(')(a)=lim_(h->0)(f(a+h)-f(a))/(h)
Now find the slope of the tangent line to the graph of f at the point (1,6) using the alternate equation given below.
f^(')(a)=lim_(x->a)(f(x)-f(a))/(x-a)
(b) Use your results in part (a) to write an equation for the tangent line.
y=
(c) Use technology to graph f and the tangent line in the same viewing window.
Explain the relationship between the graph of f and the tangent line as you zoom in near the point (1,6).
Let f(x)=7x-x2 aFind the slope of the tangent line to the graph of f at the point 1,6 using the definition given below fa+h-a h
Now find the slope of the tangent line to the graph of f at the point 1,6using the alternate equation given below fa=lim f(x-fa x-a
b Use your results in part ato write an equation for the tangent line =5x+1
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Explain the relationship between the graph of f and the tangent line as you zoom in near the point 1,6
