SOLUTION: a) Determine the general equation, in simplified form, for the slope of the secant line on the graph of f(x) = x^2 between the point with x-coordinate a = 3, and the point (a + h,
Question 1176207: a) Determine the general equation, in simplified form, for the slope of the secant line on the graph of f(x) = x^2 between the point with x-coordinate a = 3, and the point (a + h, f(a + h)). Do not use a specific value of h.
b) Use the result of part a) to estimate the slope of the tangent line at the point with x-coordinate 3. Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
Hi
f(x) = x^2 and f(3+h) = (3+h)^2 = 9 + 6h + h^2
slope secant line at x = 3 :
(f(3+h) - f(3))/h = (6h+ h^2)/h = 6 + h
at x = 3, slope = 6+h
And as h ⇒ 0, slope approaches 6
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